2.61/1.72	WORST_CASE(?, O(n^1))
2.61/1.73	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.61/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.73	
2.61/1.73	
2.61/1.73	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.61/1.73	
2.61/1.73	(0) CpxIntTrs
2.61/1.73	(1) Koat Proof [FINISHED, 478 ms]
2.61/1.73	(2) BOUNDS(1, n^1)
2.61/1.73	
2.61/1.73	
2.61/1.73	----------------------------------------
2.61/1.73	
2.61/1.73	(0)
2.61/1.73	Obligation:
2.61/1.73	Complexity Int TRS consisting of the following rules:
2.61/1.73	eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.61/1.73	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
2.61/1.73	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0
2.61/1.73	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 >= 0
2.61/1.73	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < 0 && v_.01 < 0
2.61/1.73	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: v_.0 >= 0
2.61/1.73	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0 && v_.0 < 0
2.61/1.73	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 < 0 && v_.0 >= 0
2.61/1.73	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < 0
2.61/1.73	eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.61/1.73	
2.61/1.73	The start-symbols are:[eval_foo_start_4]
2.61/1.73	
2.61/1.73	
2.61/1.73	----------------------------------------
2.61/1.73	
2.61/1.73	(1) Koat Proof (FINISHED)
2.61/1.73	YES(?, 2*ar_3 + 5*ar_1 + 18)
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Initial complexity problem:
2.61/1.73	
2.61/1.73	1:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	2:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.61/1.73	
2.61/1.73	3:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	A polynomial rank function with
2.61/1.73	
2.61/1.73		Pol(evalfoobb3in) = 1
2.61/1.73	
2.61/1.73		Pol(evalfoostop) = 0
2.61/1.73	
2.61/1.73		Pol(evalfoobb2in) = 2
2.61/1.73	
2.61/1.73		Pol(evalfoobb1in) = 2
2.61/1.73	
2.61/1.73		Pol(evalfoobb0in) = 2
2.61/1.73	
2.61/1.73		Pol(evalfoostart) = 2
2.61/1.73	
2.61/1.73		Pol(koat_start) = 2
2.61/1.73	
2.61/1.73	orients all transitions weakly and the transitions
2.61/1.73	
2.61/1.73		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73	strictly and produces the following problem:
2.61/1.73	
2.61/1.73	4:	T:
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	A polynomial rank function with
2.61/1.73	
2.61/1.73		Pol(evalfoobb3in) = V_1
2.61/1.73	
2.61/1.73		Pol(evalfoostop) = V_1
2.61/1.73	
2.61/1.73		Pol(evalfoobb2in) = V_1 + 1
2.61/1.73	
2.61/1.73		Pol(evalfoobb1in) = V_1 + 1
2.61/1.73	
2.61/1.73		Pol(evalfoobb0in) = V_2 + 1
2.61/1.73	
2.61/1.73		Pol(evalfoostart) = V_2 + 1
2.61/1.73	
2.61/1.73		Pol(koat_start) = V_2 + 1
2.61/1.73	
2.61/1.73	orients all transitions weakly and the transition
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73	strictly and produces the following problem:
2.61/1.73	
2.61/1.73	5:	T:
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Repeatedly propagating knowledge in problem 5 produces the following problem:
2.61/1.73	
2.61/1.73	6:	T:
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Applied AI with 'oct' on problem 6 to obtain the following invariants:
2.61/1.73	
2.61/1.73	  For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.61/1.73	
2.61/1.73	  For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.61/1.73	
2.61/1.73	  For symbol evalfoobb3in: -X_3 + X_4 >= 0 /\ -X_3 - 1 >= 0 /\ -X_1 - X_3 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 - 1 >= 0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	This yielded the following problem:
2.61/1.73	
2.61/1.73	7:	T:
2.61/1.73	
2.61/1.73			(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 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 7, the following new transition is obtained:
2.61/1.73	
2.61/1.73		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	8:	T:
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Testing for reachability in the complexity graph removes the following transition from problem 8:
2.61/1.73	
2.61/1.73		evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	9:	T:
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	By chaining the transition evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ] with all transitions in problem 9, the following new transition is obtained:
2.61/1.73	
2.61/1.73		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	10:	T:
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Testing for reachability in the complexity graph removes the following transition from problem 10:
2.61/1.73	
2.61/1.73		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	11:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	By chaining the transition evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
2.61/1.73	
2.61/1.73		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	12:	T:
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 12, the following new transition is obtained:
2.61/1.73	
2.61/1.73		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	13:	T:
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Testing for reachability in the complexity graph removes the following transition from problem 13:
2.61/1.73	
2.61/1.73		evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	14:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	By chaining the transition evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ] with all transitions in problem 14, the following new transitions are obtained:
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73	We thus obtain the following problem:
2.61/1.73	
2.61/1.73	15:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 3)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 2)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Repeatedly propagating knowledge in problem 15 produces the following problem:
2.61/1.73	
2.61/1.73	16:	T:
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 3)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 2)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2*ar_1 + 4, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	A polynomial rank function with
2.61/1.73	
2.61/1.73		Pol(evalfoobb2in) = 1
2.61/1.73	
2.61/1.73		Pol(evalfoostop) = 0
2.61/1.73	
2.61/1.73		Pol(evalfoobb1in) = 1
2.61/1.73	
2.61/1.73		Pol(koat_start) = 1
2.61/1.73	
2.61/1.73	orients all transitions weakly and the transition
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73	strictly and produces the following problem:
2.61/1.73	
2.61/1.73	17:	T:
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 3)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ?, Cost: 2)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2*ar_1 + 4, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	A polynomial rank function with
2.61/1.73	
2.61/1.73		Pol(evalfoobb2in) = V_3
2.61/1.73	
2.61/1.73		Pol(evalfoostop) = V_3
2.61/1.73	
2.61/1.73		Pol(evalfoobb1in) = V_3
2.61/1.73	
2.61/1.73		Pol(koat_start) = V_4
2.61/1.73	
2.61/1.73	orients all transitions weakly and the transition
2.61/1.73	
2.61/1.73		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73	strictly and produces the following problem:
2.61/1.73	
2.61/1.73	18:	T:
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 3)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ 0 >= ar_2 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 - 1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_3, Cost: 2)          evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ -ar_2 + ar_3 + 1 >= 0 /\ ar_2 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 1, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: ar_1 + 2, Cost: 2)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2, Cost: 2)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 /\ -ar_2 - 1 >= 0 /\ -ar_0 - ar_2 - 2 >= 0 /\ -ar_0 - 1 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 2*ar_1 + 4, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 0 ]
2.61/1.73	
2.61/1.73			(Comp: 1, Cost: 2)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) [ 0 <= 0 ]
2.61/1.73	
2.61/1.73		start location:	koat_start
2.61/1.73	
2.61/1.73		leaf cost:	0
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Complexity upper bound 2*ar_3 + 5*ar_1 + 18
2.61/1.73	
2.61/1.73	
2.61/1.73	
2.61/1.73	Time: 0.486 sec (SMT: 0.405 sec)
2.61/1.73	
2.61/1.73	
2.61/1.73	----------------------------------------
2.61/1.73	
2.61/1.73	(2)
2.61/1.73	BOUNDS(1, n^1)
2.61/1.75	EOF