2.61/1.74	WORST_CASE(?, O(n^2))
2.61/1.75	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.61/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.75	
2.61/1.75	
2.61/1.75	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.61/1.75	
2.61/1.75	(0) CpxIntTrs
2.61/1.75	(1) Koat Proof [FINISHED, 476 ms]
2.61/1.75	(2) BOUNDS(1, n^2)
2.61/1.75	
2.61/1.75	
2.61/1.75	----------------------------------------
2.61/1.75	
2.61/1.75	(0)
2.61/1.75	Obligation:
2.61/1.75	Complexity Int TRS consisting of the following rules:
2.61/1.75	eval_ex_paper1_start(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb0_in(v_.0, v_fwd, v_i, v_n)) :|: TRUE
2.61/1.75	eval_ex_paper1_bb0_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb1_in(v_i, v_fwd, v_i, v_n)) :|: TRUE
2.61/1.75	eval_ex_paper1_bb1_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb2_in(v_.0, v_fwd, v_i, v_n)) :|: 0 < v_.0 && v_.0 < v_n
2.61/1.75	eval_ex_paper1_bb1_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb3_in(v_.0, v_fwd, v_i, v_n)) :|: 0 >= v_.0
2.61/1.75	eval_ex_paper1_bb1_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb3_in(v_.0, v_fwd, v_i, v_n)) :|: v_.0 >= v_n
2.61/1.75	eval_ex_paper1_bb2_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb1_in(v_.0 + 1, v_fwd, v_i, v_n)) :|: v_fwd > 0
2.61/1.75	eval_ex_paper1_bb2_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_bb1_in(v_.0 - 1, v_fwd, v_i, v_n)) :|: v_fwd <= 0
2.61/1.75	eval_ex_paper1_bb3_in(v_.0, v_fwd, v_i, v_n) -> Com_1(eval_ex_paper1_stop(v_.0, v_fwd, v_i, v_n)) :|: TRUE
2.61/1.75	
2.61/1.75	The start-symbols are:[eval_ex_paper1_start_4]
2.61/1.75	
2.61/1.75	
2.61/1.75	----------------------------------------
2.61/1.75	
2.61/1.75	(1) Koat Proof (FINISHED)
2.61/1.75	YES(?, 4*ar_1^2 + 4*ar_1*ar_2 + 4*ar_1 + 13)
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Initial complexity problem:
2.61/1.75	
2.61/1.75	1:	T:
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.61/1.75	
2.61/1.75	2:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	A polynomial rank function with
2.61/1.75	
2.61/1.75		Pol(evalexpaper1start) = 2
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb0in) = 2
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb1in) = 2
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb2in) = 2
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb3in) = 1
2.61/1.75	
2.61/1.75		Pol(evalexpaper1stop) = 0
2.61/1.75	
2.61/1.75		Pol(koat_start) = 2
2.61/1.75	
2.61/1.75	orients all transitions weakly and the transitions
2.61/1.75	
2.61/1.75		evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75	strictly and produces the following problem:
2.61/1.75	
2.61/1.75	3:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.61/1.75	
2.61/1.75	  For symbol evalexpaper1bb2in: X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	This yielded the following problem:
2.61/1.75	
2.61/1.75	4:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
2.61/1.75	
2.61/1.75		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	5:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Testing for reachability in the complexity graph removes the following transition from problem 5:
2.61/1.75	
2.61/1.75		evalexpaper1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	6:	T:
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	By chaining the transition evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] with all transitions in problem 6, the following new transition is obtained:
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	7:	T:
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	By chaining the transition evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] with all transitions in problem 7, the following new transition is obtained:
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	8:	T:
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 1)    evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Testing for reachability in the complexity graph removes the following transition from problem 8:
2.61/1.75	
2.61/1.75		evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	9:	T:
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 9, the following new transition is obtained:
2.61/1.75	
2.61/1.75		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	10:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 1)    evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	Testing for reachability in the complexity graph removes the following transition from problem 10:
2.61/1.75	
2.61/1.75		evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3))
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	11:	T:
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	By chaining the transition evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] with all transitions in problem 11, the following new transitions are obtained:
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.75	We thus obtain the following problem:
2.61/1.75	
2.61/1.75	12:	T:
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 3)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 2)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	A polynomial rank function with
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb2in) = 1
2.61/1.75	
2.61/1.75		Pol(evalexpaper1stop) = 0
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb1in) = 1
2.61/1.75	
2.61/1.75		Pol(koat_start) = 1
2.61/1.75	
2.61/1.75	orients all transitions weakly and the transition
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.75	
2.61/1.75	strictly and produces the following problem:
2.61/1.75	
2.61/1.75	13:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 3)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 2)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	A polynomial rank function with
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb2in) = 2*V_1 - 1
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb1in) = 2*V_1
2.61/1.75	
2.61/1.75	and size complexities
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-0) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-0) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75	orients the transitions
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75	weakly and the transitions
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75		evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75	strictly and produces the following problem:
2.61/1.75	
2.61/1.75	14:	T:
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 3)         evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: ?, Cost: 2)         evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.75			(Comp: 2*ar_1, Cost: 1)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)         evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.75	
2.61/1.75			(Comp: 2, Cost: 2)         evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.75	
2.61/1.75			(Comp: 2*ar_1, Cost: 1)    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.75	
2.61/1.75			(Comp: 1, Cost: 2)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.75	
2.61/1.75		start location:	koat_start
2.61/1.75	
2.61/1.75		leaf cost:	0
2.61/1.75	
2.61/1.75	
2.61/1.75	
2.61/1.75	A polynomial rank function with
2.61/1.75	
2.61/1.75		Pol(evalexpaper1bb2in) = -V_1 + V_3
2.61/1.75	
2.61/1.75	and size complexities
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-0) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= 1 /\\ ar_2 >= ar_0 + 2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-0) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-1) = ar_1
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-2) = ar_2
2.61/1.75	
2.61/1.75		S("evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 /\\ ar_0 + 1 >= ar_2 ]", 0-3) = ar_3
2.61/1.75	
2.61/1.75	orients the transitions
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.75	weakly and the transition
2.61/1.75	
2.61/1.75		evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.75	
2.61/1.76	strictly and produces the following problem:
2.61/1.76	
2.61/1.76	15:	T:
2.61/1.76	
2.61/1.76			(Comp: 1, Cost: 3)                         evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= ar_2 ]
2.61/1.76	
2.61/1.76			(Comp: 2*ar_1^2 + 2*ar_1*ar_2, Cost: 2)    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 /\ ar_0 + 1 >= 1 /\ ar_2 >= ar_0 + 2 ]
2.61/1.76	
2.61/1.76			(Comp: 2*ar_1, Cost: 1)                    evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
2.61/1.76	
2.61/1.76			(Comp: 2, Cost: 2)                         evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.61/1.76	
2.61/1.76			(Comp: 2, Cost: 2)                         evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.76	
2.61/1.76			(Comp: 2*ar_1, Cost: 1)                    evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.61/1.76	
2.61/1.76			(Comp: 1, Cost: 2)                         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalexpaper1bb1in(ar_1, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.76	
2.61/1.76		start location:	koat_start
2.61/1.76	
2.61/1.76		leaf cost:	0
2.61/1.76	
2.61/1.76	
2.61/1.76	
2.61/1.76	Complexity upper bound 4*ar_1^2 + 4*ar_1*ar_2 + 4*ar_1 + 13
2.61/1.76	
2.61/1.76	
2.61/1.76	
2.61/1.76	Time: 0.459 sec (SMT: 0.374 sec)
2.61/1.76	
2.61/1.76	
2.61/1.76	----------------------------------------
2.61/1.76	
2.61/1.76	(2)
2.61/1.76	BOUNDS(1, n^2)
2.61/1.77	EOF