2.61/1.61	WORST_CASE(?, O(n^2))
2.61/1.62	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.61/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.62	
2.61/1.62	
2.61/1.62	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.61/1.62	
2.61/1.62	(0) CpxIntTrs
2.61/1.62	(1) Koat Proof [FINISHED, 278 ms]
2.61/1.62	(2) BOUNDS(1, n^2)
2.61/1.62	
2.61/1.62	
2.61/1.62	----------------------------------------
2.61/1.62	
2.61/1.62	(0)
2.61/1.62	Obligation:
2.61/1.62	Complexity Int TRS consisting of the following rules:
2.61/1.62	eval_foo_start(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: TRUE
2.61/1.62	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb1_in(0, 0, v_i, v_j, v_m, v_n)) :|: v_m > 0 && v_n > v_m
2.61/1.62	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: v_m <= 0
2.61/1.62	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: v_n <= v_m
2.61/1.62	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: v_.0 < v_n
2.61/1.62	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: v_.0 >= v_n
2.61/1.62	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 + 1, v_i, v_j, v_m, v_n)) :|: v_.01 < v_m
2.61/1.62	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 + 1, v_i, v_j, v_m, v_n)) :|: v_.01 < v_m && v_.01 >= v_m
2.61/1.62	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0, 0, v_i, v_j, v_m, v_n)) :|: v_.01 >= v_m && v_.01 < v_m
2.61/1.62	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0 + 1, 0, v_i, v_j, v_m, v_n)) :|: v_.01 >= v_m
2.61/1.62	eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_m, v_n) -> Com_1(eval_foo_stop(v_.0, v_.01, v_i, v_j, v_m, v_n)) :|: TRUE
2.61/1.62	
2.61/1.62	The start-symbols are:[eval_foo_start_6]
2.61/1.62	
2.61/1.62	
2.61/1.62	----------------------------------------
2.61/1.62	
2.61/1.62	(1) Koat Proof (FINISHED)
2.61/1.62	YES(?, 2*ar_1 + 2*ar_0*ar_1 + 2*ar_0 + 9)
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Initial complexity problem:
2.61/1.62	
2.61/1.62	1:	T:
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, 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_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62	We thus obtain the following problem:
2.61/1.62	
2.61/1.62	2:	T:
2.61/1.62	
2.61/1.62			(Comp: ?, 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_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.61/1.62	
2.61/1.62	3:	T:
2.61/1.62	
2.61/1.62			(Comp: ?, 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_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	A polynomial rank function with
2.61/1.62	
2.61/1.62		Pol(evalfoobb1in) = 2
2.61/1.62	
2.61/1.62		Pol(evalfoobb3in) = 1
2.61/1.62	
2.61/1.62		Pol(evalfoobb2in) = 2
2.61/1.62	
2.61/1.62		Pol(evalfoostop) = 0
2.61/1.62	
2.61/1.62		Pol(evalfoobb0in) = 2
2.61/1.62	
2.61/1.62		Pol(evalfoostart) = 2
2.61/1.62	
2.61/1.62		Pol(koat_start) = 2
2.61/1.62	
2.61/1.62	orients all transitions weakly and the transitions
2.61/1.62	
2.61/1.62		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
2.61/1.62	
2.61/1.62	strictly and produces the following problem:
2.61/1.62	
2.61/1.62	4:	T:
2.61/1.62	
2.61/1.62			(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_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.61/1.62	
2.61/1.62	  For symbol evalfoobb1in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.61/1.62	
2.61/1.62	  For symbol evalfoobb2in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	This yielded the following problem:
2.61/1.62	
2.61/1.62	5:	T:
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(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_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	A polynomial rank function with
2.61/1.62	
2.61/1.62		Pol(evalfoobb2in) = V_2 - V_3
2.61/1.62	
2.61/1.62		Pol(evalfoobb1in) = V_2 - V_3
2.61/1.62	
2.61/1.62	and size complexities
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_1 + ar_2
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62	orients the transitions
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62	weakly and the transition
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62	strictly and produces the following problem:
2.61/1.62	
2.61/1.62	6:	T:
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)       evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 2, Cost: 1)       evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(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_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	A polynomial rank function with
2.61/1.62	
2.61/1.62		Pol(evalfoobb2in) = V_1 - V_4
2.61/1.62	
2.61/1.62		Pol(evalfoobb1in) = V_1 - V_4
2.61/1.62	
2.61/1.62	and size complexities
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_1 + ar_2
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = 0
2.61/1.62	
2.61/1.62		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = 0
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62		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
2.61/1.62	
2.61/1.62	orients the transitions
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62	weakly and the transition
2.61/1.62	
2.61/1.62		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62	strictly and produces the following problem:
2.61/1.62	
2.61/1.62	7:	T:
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                   evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                   evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                   evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                   evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ?, Cost: 1)                   evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 2, Cost: 1)                   evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ar_0*ar_1 + ar_0, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ar_1, Cost: 1)                evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(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_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.61/1.62	
2.61/1.62	8:	T:
2.61/1.62	
2.61/1.62			(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 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                              evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                              evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                              evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.62	
2.61/1.62			(Comp: 1, Cost: 1)                              evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.62	
2.61/1.62			(Comp: ar_1 + ar_0*ar_1 + ar_0 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: 2, Cost: 1)                              evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.62	
2.61/1.62			(Comp: ar_0*ar_1 + ar_0, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.61/1.62	
2.61/1.62			(Comp: ar_1, Cost: 1)                           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.61/1.62	
2.61/1.62			(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_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
2.61/1.62	
2.61/1.62		start location:	koat_start
2.61/1.62	
2.61/1.62		leaf cost:	0
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Complexity upper bound 2*ar_1 + 2*ar_0*ar_1 + 2*ar_0 + 9
2.61/1.62	
2.61/1.62	
2.61/1.62	
2.61/1.62	Time: 0.303 sec (SMT: 0.241 sec)
2.61/1.62	
2.61/1.62	
2.61/1.62	----------------------------------------
2.61/1.62	
2.61/1.62	(2)
2.61/1.62	BOUNDS(1, n^2)
2.61/1.64	EOF