2.10/1.45	WORST_CASE(?, O(n^1))
2.28/1.46	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.28/1.46	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.28/1.46	
2.28/1.46	
2.28/1.46	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.28/1.46	
2.28/1.46	(0) CpxIntTrs
2.28/1.46	(1) Koat Proof [FINISHED, 183 ms]
2.28/1.46	(2) BOUNDS(1, n^1)
2.28/1.46	
2.28/1.46	
2.28/1.46	----------------------------------------
2.28/1.46	
2.28/1.46	(0)
2.28/1.46	Obligation:
2.28/1.46	Complexity Int TRS consisting of the following rules:
2.28/1.46	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
2.28/1.46	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)) :|: v_x >= 0 && v_y >= 0
2.28/1.46	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_x < 0
2.28/1.46	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_y < 0
2.28/1.46	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 > 2
2.28/1.46	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 - v_.0 > 2
2.28/1.46	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 - v_.01 <= 2 && v_.01 - v_.0 <= 2
2.28/1.46	eval_foo_.critedge_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 < v_.01
2.28/1.46	eval_foo_.critedge_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 < v_.01 && v_.0 >= v_.01
2.28/1.46	eval_foo_.critedge_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 >= v_.01 && v_.0 < v_.01
2.28/1.46	eval_foo_.critedge_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 >= v_.01
2.28/1.46	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.28/1.46	
2.28/1.46	The start-symbols are:[eval_foo_start_4]
2.28/1.46	
2.28/1.46	
2.28/1.46	----------------------------------------
2.28/1.46	
2.28/1.46	(1) Koat Proof (FINISHED)
2.28/1.46	YES(?, 8*ar_0 + 8*ar_1 + 14)
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	Initial complexity problem:
2.28/1.46	
2.28/1.46	1:	T:
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46	We thus obtain the following problem:
2.28/1.46	
2.28/1.46	2:	T:
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.28/1.46	
2.28/1.46	3:	T:
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	A polynomial rank function with
2.28/1.46	
2.28/1.46		Pol(evalfoocritedgein) = 2
2.28/1.46	
2.28/1.46		Pol(evalfoobb1in) = 2
2.28/1.46	
2.28/1.46		Pol(evalfoobb2in) = 1
2.28/1.46	
2.28/1.46		Pol(evalfoostop) = 0
2.28/1.46	
2.28/1.46		Pol(evalfoobb0in) = 2
2.28/1.46	
2.28/1.46		Pol(evalfoostart) = 2
2.28/1.46	
2.28/1.46		Pol(koat_start) = 2
2.28/1.46	
2.28/1.46	orients all transitions weakly and the transitions
2.28/1.46	
2.28/1.46		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46	strictly and produces the following problem:
2.28/1.46	
2.28/1.46	4:	T:
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	A polynomial rank function with
2.28/1.46	
2.28/1.46		Pol(evalfoobb1in) = -2*V_3 + 2*V_4 + 1
2.28/1.46	
2.28/1.46		Pol(evalfoocritedgein) = -2*V_3 + 2*V_4
2.28/1.46	
2.28/1.46	and size complexities
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-2) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-2) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-2) = ?
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46	orients the transitions
2.28/1.46	
2.28/1.46		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46	weakly and the transitions
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46	strictly and produces the following problem:
2.28/1.46	
2.28/1.46	5:	T:
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)                      evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: ?, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	A polynomial rank function with
2.28/1.46	
2.28/1.46		Pol(evalfoocritedgein) = 2*V_3 - 2*V_4 + 1
2.28/1.46	
2.28/1.46		Pol(evalfoobb1in) = 2*V_3 - 2*V_4 + 2
2.28/1.46	
2.28/1.46	and size complexities
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-2) = ar_2
2.28/1.46	
2.28/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-3) = ar_3
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-2) = 3*ar_0 + 3*ar_1 + 9
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-2) = 3*ar_0 + 3*ar_1 + 27
2.28/1.46	
2.28/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 3*ar_0 + 3*ar_1 + 3*ar_2 + 81
2.28/1.46	
2.28/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-2) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-3) = ?
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ar_0
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ar_1
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-2) = 3*ar_0 + 3*ar_1 + 9
2.28/1.46	
2.28/1.46		S("evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ar_1
2.28/1.46	
2.28/1.46	orients the transitions
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46	weakly and the transitions
2.28/1.46	
2.28/1.46		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46	strictly and produces the following problem:
2.28/1.46	
2.28/1.46	6:	T:
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(Comp: 2, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
2.28/1.46	
2.28/1.46			(Comp: 1, Cost: 1)                      evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.28/1.46	
2.28/1.46			(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 ]
2.28/1.46	
2.28/1.46		start location:	koat_start
2.28/1.46	
2.28/1.46		leaf cost:	0
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	Complexity upper bound 8*ar_0 + 8*ar_1 + 14
2.28/1.46	
2.28/1.46	
2.28/1.46	
2.28/1.46	Time: 0.133 sec (SMT: 0.112 sec)
2.28/1.46	
2.28/1.46	
2.28/1.46	----------------------------------------
2.28/1.46	
2.28/1.46	(2)
2.28/1.46	BOUNDS(1, n^1)
2.28/1.49	EOF