2.49/1.44	WORST_CASE(?, O(n^2))
2.49/1.45	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.49/1.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.49/1.45	
2.49/1.45	
2.49/1.45	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.49/1.45	
2.49/1.45	(0) CpxIntTrs
2.49/1.45	(1) Koat Proof [FINISHED, 179 ms]
2.49/1.45	(2) BOUNDS(1, n^2)
2.49/1.45	
2.49/1.45	
2.49/1.45	----------------------------------------
2.49/1.45	
2.49/1.45	(0)
2.49/1.45	Obligation:
2.49/1.45	Complexity Int TRS consisting of the following rules:
2.49/1.45	eval_cousot9_start(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb0_in(v_.0, v_N, v_i.0, v_j)) :|: TRUE
2.49/1.45	eval_cousot9_bb0_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_j, v_N, v_N, v_j)) :|: TRUE
2.49/1.45	eval_cousot9_bb1_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j)) :|: v_i.0 > 0
2.49/1.45	eval_cousot9_bb1_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb3_in(v_.0, v_N, v_i.0, v_j)) :|: v_i.0 <= 0
2.49/1.45	eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_.0 - 1, v_N, v_i.0, v_j)) :|: v_.0 > 0
2.49/1.45	eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_N, v_N, v_i.0, v_j)) :|: v_.0 > 0 && v_.0 <= 0
2.49/1.45	eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_.0 - 1, v_N, v_i.0 - 1, v_j)) :|: v_.0 <= 0 && v_.0 > 0
2.49/1.45	eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_N, v_N, v_i.0 - 1, v_j)) :|: v_.0 <= 0
2.49/1.45	eval_cousot9_bb3_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_stop(v_.0, v_N, v_i.0, v_j)) :|: TRUE
2.49/1.45	
2.49/1.45	The start-symbols are:[eval_cousot9_start_4]
2.49/1.45	
2.49/1.45	
2.49/1.45	----------------------------------------
2.49/1.45	
2.49/1.45	(1) Koat Proof (FINISHED)
2.49/1.45	YES(?, 2*ar_3 + 2*ar_3^2 + 2*ar_1 + 7)
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Initial complexity problem:
2.49/1.45	
2.49/1.45	1:	T:
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.49/1.45	
2.49/1.45		evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45		evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45	We thus obtain the following problem:
2.49/1.45	
2.49/1.45	2:	T:
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.49/1.45	
2.49/1.45	3:	T:
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	A polynomial rank function with
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb3in) = 1
2.49/1.45	
2.49/1.45		Pol(evalcousot9stop) = 0
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb2in) = 2
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb1in) = 2
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb0in) = 2
2.49/1.45	
2.49/1.45		Pol(evalcousot9start) = 2
2.49/1.45	
2.49/1.45		Pol(koat_start) = 2
2.49/1.45	
2.49/1.45	orients all transitions weakly and the transitions
2.49/1.45	
2.49/1.45		evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45		evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45	strictly and produces the following problem:
2.49/1.45	
2.49/1.45	4:	T:
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)    evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.49/1.45	
2.49/1.45	  For symbol evalcousot9bb1in: -X_3 + X_4 >= 0
2.49/1.45	
2.49/1.45	  For symbol evalcousot9bb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_3 - 1 >= 0
2.49/1.45	
2.49/1.45	  For symbol evalcousot9bb3in: -X_3 + X_4 >= 0 /\ -X_3 >= 0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	This yielded the following problem:
2.49/1.45	
2.49/1.45	5:	T:
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)    evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)    evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 >= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	A polynomial rank function with
2.49/1.45	
2.49/1.45		Pol(koat_start) = V_4
2.49/1.45	
2.49/1.45		Pol(evalcousot9start) = V_4
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb0in) = V_4
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb1in) = V_3
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb2in) = V_3
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb3in) = V_3
2.49/1.45	
2.49/1.45		Pol(evalcousot9stop) = V_3
2.49/1.45	
2.49/1.45	orients all transitions weakly and the transition
2.49/1.45	
2.49/1.45		evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45	strictly and produces the following problem:
2.49/1.45	
2.49/1.45	6:	T:
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)       evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)       evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)       evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)       evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)       evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ar_3, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)       evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 >= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	A polynomial rank function with
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb2in) = V_1
2.49/1.45	
2.49/1.45		Pol(evalcousot9bb1in) = V_1
2.49/1.45	
2.49/1.45	and size complexities
2.49/1.45	
2.49/1.45		S("evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_2 >= 0 ]", 0-0) = ar_1 + ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_2 >= 0 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_2 >= 0 ]", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_2 >= 0 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ 0 >= ar_0 ]", 0-0) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ 0 >= ar_0 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ 0 >= ar_0 ]", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ 0 >= ar_0 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-0) = ar_1 + ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_1 + ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_1 + ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.49/1.45	
2.49/1.45		S("evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.49/1.45	
2.49/1.45		S("evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.49/1.45	
2.49/1.45		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.49/1.45	
2.49/1.45		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.49/1.45	
2.49/1.45		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.49/1.45	
2.49/1.45		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.49/1.45	
2.49/1.45	orients the transitions
2.49/1.45	
2.49/1.45		evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45		evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45	weakly and the transition
2.49/1.45	
2.49/1.45		evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45	strictly and produces the following problem:
2.49/1.45	
2.49/1.45	7:	T:
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)                koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)                evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)                evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ?, Cost: 1)                evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)                evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ar_3^2 + ar_1, Cost: 1)    evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ar_3, Cost: 1)             evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)                evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 >= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.49/1.45	
2.49/1.45	8:	T:
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)                           evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3))
2.49/1.45	
2.49/1.45			(Comp: 1, Cost: 1)                           evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3))
2.49/1.45	
2.49/1.45			(Comp: ar_3 + ar_3^2 + ar_1 + 1, Cost: 1)    evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)                           evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ]
2.49/1.45	
2.49/1.45			(Comp: ar_3^2 + ar_1, Cost: 1)               evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 >= 1 ]
2.49/1.45	
2.49/1.45			(Comp: ar_3, Cost: 1)                        evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ 0 >= ar_0 ]
2.49/1.45	
2.49/1.45			(Comp: 2, Cost: 1)                           evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 >= 0 ]
2.49/1.45	
2.49/1.45		start location:	koat_start
2.49/1.45	
2.49/1.45		leaf cost:	0
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Complexity upper bound 2*ar_3 + 2*ar_3^2 + 2*ar_1 + 7
2.49/1.45	
2.49/1.45	
2.49/1.45	
2.49/1.45	Time: 0.210 sec (SMT: 0.188 sec)
2.49/1.45	
2.49/1.45	
2.49/1.45	----------------------------------------
2.49/1.45	
2.49/1.45	(2)
2.49/1.45	BOUNDS(1, n^2)
2.49/1.48	EOF