2.37/1.51	WORST_CASE(?, O(n^1))
2.37/1.52	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.37/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.37/1.52	
2.37/1.52	
2.37/1.52	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.37/1.52	
2.37/1.52	(0) CpxIntTrs
2.37/1.52	(1) Koat Proof [FINISHED, 279 ms]
2.37/1.52	(2) BOUNDS(1, n^1)
2.37/1.52	
2.37/1.52	
2.37/1.52	----------------------------------------
2.37/1.52	
2.37/1.52	(0)
2.37/1.52	Obligation:
2.37/1.52	Complexity Int TRS consisting of the following rules:
2.37/1.52	eval_foo_start(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y, v_z)) :|: TRUE
2.37/1.52	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_x, v_z, v_x, v_y, v_z)) :|: TRUE
2.37/1.52	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y, v_z)) :|: v_.0 < v_y
2.37/1.52	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y, v_z)) :|: v_.0 >= v_y
2.37/1.52	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_x, v_y, v_z)) :|: v_.0 < v_.01
2.37/1.52	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y, v_z)) :|: v_.0 < v_.01 && v_.0 >= v_.01
2.37/1.53	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 + 1, v_x, v_y, v_z)) :|: v_.0 >= v_.01 && v_.0 < v_.01
2.37/1.53	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 + 1, v_x, v_y, v_z)) :|: v_.0 >= v_.01
2.37/1.53	eval_foo_bb3_in(v_.0, v_.01, v_x, v_y, v_z) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y, v_z)) :|: TRUE
2.37/1.53	
2.37/1.53	The start-symbols are:[eval_foo_start_5]
2.37/1.53	
2.37/1.53	
2.37/1.53	----------------------------------------
2.37/1.53	
2.37/1.53	(1) Koat Proof (FINISHED)
2.37/1.53	YES(?, 2*ar_3 + 4*ar_4 + 2*ar_1 + 7)
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Initial complexity problem:
2.37/1.53	
2.37/1.53	1:	T:
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.37/1.53	
2.37/1.53		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53	We thus obtain the following problem:
2.37/1.53	
2.37/1.53	2:	T:
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.37/1.53	
2.37/1.53	3:	T:
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	A polynomial rank function with
2.37/1.53	
2.37/1.53		Pol(evalfoobb3in) = 1
2.37/1.53	
2.37/1.53		Pol(evalfoostop) = 0
2.37/1.53	
2.37/1.53		Pol(evalfoobb2in) = 2
2.37/1.53	
2.37/1.53		Pol(evalfoobb1in) = 2
2.37/1.53	
2.37/1.53		Pol(evalfoobb0in) = 2
2.37/1.53	
2.37/1.53		Pol(evalfoostart) = 2
2.37/1.53	
2.37/1.53		Pol(koat_start) = 2
2.37/1.53	
2.37/1.53	orients all transitions weakly and the transitions
2.37/1.53	
2.37/1.53		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53	strictly and produces the following problem:
2.37/1.53	
2.37/1.53	4:	T:
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.37/1.53	
2.37/1.53	  For symbol evalfoobb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.37/1.53	
2.37/1.53	  For symbol evalfoobb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.37/1.53	
2.37/1.53	  For symbol evalfoobb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	This yielded the following problem:
2.37/1.53	
2.37/1.53	5:	T:
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	A polynomial rank function with
2.37/1.53	
2.37/1.53		Pol(koat_start) = -V_2 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoostart) = -V_2 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb0in) = -V_2 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb1in) = -V_1 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb2in) = -V_1 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb3in) = -V_1 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoostop) = -V_1 + V_5
2.37/1.53	
2.37/1.53	orients all transitions weakly and the transition
2.37/1.53	
2.37/1.53		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53	strictly and produces the following problem:
2.37/1.53	
2.37/1.53	6:	T:
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ar_1 + ar_4, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	A polynomial rank function with
2.37/1.53	
2.37/1.53		Pol(koat_start) = -V_4 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoostart) = -V_4 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb0in) = -V_4 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb1in) = -V_3 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb2in) = -V_3 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoobb3in) = -V_3 + V_5
2.37/1.53	
2.37/1.53		Pol(evalfoostop) = -V_3 + V_5
2.37/1.53	
2.37/1.53	orients all transitions weakly and the transition
2.37/1.53	
2.37/1.53		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53	strictly and produces the following problem:
2.37/1.53	
2.37/1.53	7:	T:
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ?, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ar_1 + ar_4, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ar_3 + ar_4, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.37/1.53	
2.37/1.53	8:	T:
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)                           evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: 1, Cost: 1)                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.37/1.53	
2.37/1.53			(Comp: ar_3 + 2*ar_4 + ar_1 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.37/1.53	
2.37/1.53			(Comp: ar_1 + ar_4, Cost: 1)                 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.37/1.53	
2.37/1.53			(Comp: ar_3 + ar_4, Cost: 1)                 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.37/1.53	
2.37/1.53			(Comp: 2, Cost: 1)                           evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.37/1.53	
2.37/1.53		start location:	koat_start
2.37/1.53	
2.37/1.53		leaf cost:	0
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Complexity upper bound 2*ar_3 + 4*ar_4 + 2*ar_1 + 7
2.37/1.53	
2.37/1.53	
2.37/1.53	
2.37/1.53	Time: 0.226 sec (SMT: 0.191 sec)
2.37/1.53	
2.37/1.53	
2.37/1.53	----------------------------------------
2.37/1.53	
2.37/1.53	(2)
2.37/1.53	BOUNDS(1, n^1)
2.40/1.55	EOF