4.84/2.80	WORST_CASE(NON_POLY, ?)
4.86/2.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.86/2.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.86/2.81	
4.86/2.81	
4.86/2.81	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(EXP, EXP).
4.86/2.81	
4.86/2.81	(0) CpxIntTrs
4.86/2.81	(1) Koat Proof [FINISHED, 16 ms]
4.86/2.81	(2) BOUNDS(1, EXP)
4.86/2.81	(3) Loat Proof [FINISHED, 1232 ms]
4.86/2.81	(4) BOUNDS(EXP, INF)
4.86/2.81	
4.86/2.81	
4.86/2.81	----------------------------------------
4.86/2.81	
4.86/2.81	(0)
4.86/2.81	Obligation:
4.86/2.81	Complexity Int TRS consisting of the following rules:
4.86/2.81	f(A, B) -> Com_1(g(A, B)) :|: TRUE
4.86/2.81	g(A, B) -> Com_1(g(2 * A, B - 1)) :|: B > 0
4.86/2.81	g(A, B) -> Com_1(h(A, B)) :|: 0 >= B
4.86/2.81	h(A, B) -> Com_1(h(A - 1, B)) :|: A > 0
4.86/2.81	
4.86/2.81	The start-symbols are:[f_2]
4.86/2.81	
4.86/2.81	
4.86/2.81	----------------------------------------
4.86/2.81	
4.86/2.81	(1) Koat Proof (FINISHED)
4.86/2.81	YES(?, pow(2, ar_0) * ar_1 + ar_0 + ar_1 + 2)
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Initial complexity problem:
4.86/2.81	
4.86/2.81	1:	T:
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]
4.86/2.81	
4.86/2.81		start location:	koat_start
4.86/2.81	
4.86/2.81		leaf cost:	0
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.86/2.81	
4.86/2.81	2:	T:
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)    f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]
4.86/2.81	
4.86/2.81		start location:	koat_start
4.86/2.81	
4.86/2.81		leaf cost:	0
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	A polynomial rank function with
4.86/2.81	
4.86/2.81		Pol(f) = 1
4.86/2.81	
4.86/2.81		Pol(g) = 1
4.86/2.81	
4.86/2.81		Pol(h) = 0
4.86/2.81	
4.86/2.81		Pol(koat_start) = 1
4.86/2.81	
4.86/2.81	orients all transitions weakly and the transition
4.86/2.81	
4.86/2.81		g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81	strictly and produces the following problem:
4.86/2.81	
4.86/2.81	3:	T:
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)    f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)    g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)    h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]
4.86/2.81	
4.86/2.81		start location:	koat_start
4.86/2.81	
4.86/2.81		leaf cost:	0
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	A polynomial rank function with
4.86/2.81	
4.86/2.81		Pol(f) = V_1
4.86/2.81	
4.86/2.81		Pol(g) = V_1
4.86/2.81	
4.86/2.81		Pol(h) = V_1
4.86/2.81	
4.86/2.81		Pol(koat_start) = V_1
4.86/2.81	
4.86/2.81	orients all transitions weakly and the transition
4.86/2.81	
4.86/2.81		g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81	strictly and produces the following problem:
4.86/2.81	
4.86/2.81	4:	T:
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)       f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))
4.86/2.81	
4.86/2.81			(Comp: ar_0, Cost: 1)    g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)       g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81			(Comp: ?, Cost: 1)       h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]
4.86/2.81	
4.86/2.81		start location:	koat_start
4.86/2.81	
4.86/2.81		leaf cost:	0
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	A polynomial rank function with
4.86/2.81	
4.86/2.81		Pol(h) = V_2
4.86/2.81	
4.86/2.81	and size complexities
4.86/2.81	
4.86/2.81		S("koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
4.86/2.81	
4.86/2.81		S("koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
4.86/2.81	
4.86/2.81		S("h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]", 0-0) = ar_0
4.86/2.81	
4.86/2.81		S("h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]", 0-1) = pow(2, ar_0) * ar_1 + ar_1
4.86/2.81	
4.86/2.81		S("g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]", 0-0) = ar_0
4.86/2.81	
4.86/2.81		S("g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]", 0-1) = pow(2, ar_0) * ar_1 + ar_1
4.86/2.81	
4.86/2.81		S("g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]", 0-0) = ar_0
4.86/2.81	
4.86/2.81		S("g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]", 0-1) = pow(2, ar_0) * ar_1
4.86/2.81	
4.86/2.81		S("f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))", 0-0) = ar_0
4.86/2.81	
4.86/2.81		S("f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))", 0-1) = ar_1
4.86/2.81	
4.86/2.81	orients the transitions
4.86/2.81	
4.86/2.81		h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81	weakly and the transition
4.86/2.81	
4.86/2.81		h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81	strictly and produces the following problem:
4.86/2.81	
4.86/2.81	5:	T:
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)                             f(ar_0, ar_1) -> Com_1(g(ar_0, ar_1))
4.86/2.81	
4.86/2.81			(Comp: ar_0, Cost: 1)                          g(ar_0, ar_1) -> Com_1(g(ar_0 - 1, 2*ar_1)) [ ar_0 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 1)                             g(ar_0, ar_1) -> Com_1(h(ar_0, ar_1)) [ 0 >= ar_0 ]
4.86/2.81	
4.86/2.81			(Comp: pow(2, ar_0) * ar_1 + ar_1, Cost: 1)    h(ar_0, ar_1) -> Com_1(h(ar_0, ar_1 - 1)) [ ar_1 >= 1 ]
4.86/2.81	
4.86/2.81			(Comp: 1, Cost: 0)                             koat_start(ar_0, ar_1) -> Com_1(f(ar_0, ar_1)) [ 0 <= 0 ]
4.86/2.81	
4.86/2.81		start location:	koat_start
4.86/2.81	
4.86/2.81		leaf cost:	0
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Complexity upper bound pow(2, ar_0) * ar_1 + ar_0 + ar_1 + 2
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Time: 0.099 sec (SMT: 0.093 sec)
4.86/2.81	
4.86/2.81	
4.86/2.81	----------------------------------------
4.86/2.81	
4.86/2.81	(2)
4.86/2.81	BOUNDS(1, EXP)
4.86/2.81	
4.86/2.81	----------------------------------------
4.86/2.81	
4.86/2.81	(3) Loat Proof (FINISHED)
4.86/2.81	
4.86/2.81	
4.86/2.81	### Pre-processing the ITS problem ###
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Initial linear ITS problem
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      0: f -> g : [], cost: 1
4.86/2.81	
4.86/2.81	      1: g -> g : A'=-1+A, B'=2*B, [ A>=1 ], cost: 1
4.86/2.81	
4.86/2.81	      2: g -> h : [ 0>=A ], cost: 1
4.86/2.81	
4.86/2.81	      3: h -> h : B'=-1+B, [ B>=1 ], cost: 1
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	### Simplification by acceleration and chaining ###
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Accelerating simple loops of location 1.
4.86/2.81	
4.86/2.81	   Accelerating the following rules:
4.86/2.81	
4.86/2.81	      1: g -> g : A'=-1+A, B'=2*B, [ A>=1 ], cost: 1
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	   Accelerated rule 1 with metering function A, yielding the new rule 4.
4.86/2.81	
4.86/2.81	   Removing the simple loops: 1.
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Accelerating simple loops of location 2.
4.86/2.81	
4.86/2.81	   Accelerating the following rules:
4.86/2.81	
4.86/2.81	      3: h -> h : B'=-1+B, [ B>=1 ], cost: 1
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	   Accelerated rule 3 with metering function B, yielding the new rule 5.
4.86/2.81	
4.86/2.81	   Removing the simple loops: 3.
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Accelerated all simple loops using metering functions (where possible):
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      0: f -> g : [], cost: 1
4.86/2.81	
4.86/2.81	      2: g -> h : [ 0>=A ], cost: 1
4.86/2.81	
4.86/2.81	      4: g -> g : A'=0, B'=2^A*B, [ A>=1 ], cost: A
4.86/2.81	
4.86/2.81	      5: h -> h : B'=0, [ B>=1 ], cost: B
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Chained accelerated rules (with incoming rules):
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      0: f -> g : [], cost: 1
4.86/2.81	
4.86/2.81	      6: f -> g : A'=0, B'=2^A*B, [ A>=1 ], cost: 1+A
4.86/2.81	
4.86/2.81	      2: g -> h : [ 0>=A ], cost: 1
4.86/2.81	
4.86/2.81	      7: g -> h : B'=0, [ 0>=A && B>=1 ], cost: 1+B
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Removed unreachable locations (and leaf rules with constant cost):
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      0: f -> g : [], cost: 1
4.86/2.81	
4.86/2.81	      6: f -> g : A'=0, B'=2^A*B, [ A>=1 ], cost: 1+A
4.86/2.81	
4.86/2.81	      7: g -> h : B'=0, [ 0>=A && B>=1 ], cost: 1+B
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Eliminated locations (on tree-shaped paths):
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      8: f -> h : B'=0, [ 0>=A && B>=1 ], cost: 2+B
4.86/2.81	
4.86/2.81	      9: f -> h : A'=0, B'=0, [ A>=1 && 2^A*B>=1 ], cost: 2+2^A*B+A
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	### Computing asymptotic complexity ###
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Fully simplified ITS problem
4.86/2.81	
4.86/2.81	   Start location: f
4.86/2.81	
4.86/2.81	      8: f -> h : B'=0, [ 0>=A && B>=1 ], cost: 2+B
4.86/2.81	
4.86/2.81	      9: f -> h : A'=0, B'=0, [ A>=1 && 2^A*B>=1 ], cost: 2+2^A*B+A
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Computing asymptotic complexity for rule 8
4.86/2.81	
4.86/2.81	   Solved the limit problem by the following transformations:
4.86/2.81	
4.86/2.81	      Created initial limit problem:
4.86/2.81	
4.86/2.81	      2+B (+), 1-A (+/+!), B (+/+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      removing all constraints (solved by SMT)
4.86/2.81	
4.86/2.81	      resulting limit problem: [solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (C) using substitution {A==-n,B==n}
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      [solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	   Solution:
4.86/2.81	
4.86/2.81	      A / -n
4.86/2.81	
4.86/2.81	      B / n
4.86/2.81	
4.86/2.81	   Resulting cost 2+n has complexity: Poly(n^1)
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Found new complexity Poly(n^1).
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Computing asymptotic complexity for rule 9
4.86/2.81	
4.86/2.81	   Solved the limit problem by the following transformations:
4.86/2.81	
4.86/2.81	      Created initial limit problem:
4.86/2.81	
4.86/2.81	      2^A*B (+/+!), A (+/+!), 2+2^A*B+A (+) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (C) using substitution {A==1}
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      1 (+/+!), 3+2*B (+), 2*B (+/+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (B), deleting 1 (+/+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      3+2*B (+), 2*B (+/+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (D), replacing 3+2*B (+) by 2*B (+)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2*B (+) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (A), replacing 2*B (+) by B (+) and 2 (+!) using + limit vector (+,+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2 (+!), B (+) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (B), deleting 2 (+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      B (+) [solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	   Solved the limit problem by the following transformations:
4.86/2.81	
4.86/2.81	      Created initial limit problem:
4.86/2.81	
4.86/2.81	      2^A*B (+/+!), A (+/+!), 2+2^A*B+A (+) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (A), replacing 2^A*B (+/+!) by 2^A (+) and B (+!) using + limit vector (+,+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2^A (+), A (+/+!), 2+2^A*B+A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (E), replacing 2^A (+) by 1 (+/+!) and A (+)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      1 (+/+!), A (+), 2+2^A*B+A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (B), deleting 1 (+/+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      A (+), 2+2^A*B+A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (A), replacing 2+2^A*B+A (+) by 2 (+!) and 2^A*B+A (+) using + limit vector (+!,+)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2 (+!), A (+), 2^A*B+A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (B), deleting 2 (+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      A (+), 2^A*B+A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (A), replacing 2^A*B+A (+) by A (+) and 2^A*B (+) using + limit vector (+,+)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2^A*B (+), A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (A), replacing 2^A*B (+) by 2^A (+) and B (+!) using + limit vector (+,+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      2^A (+), A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (E), replacing 2^A (+) by 1 (+/+!) and A (+)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      1 (+/+!), A (+), B (+!) [not solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	      applying transformation rule (B), deleting 1 (+/+!)
4.86/2.81	
4.86/2.81	      resulting limit problem:
4.86/2.81	
4.86/2.81	      A (+), B (+!) [solved]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	   Solution:
4.86/2.81	
4.86/2.81	      A / n
4.86/2.81	
4.86/2.81	      B / 1
4.86/2.81	
4.86/2.81	   Resulting cost 2+2^n+n has complexity: Exp
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Found new complexity Exp.
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	Obtained the following overall complexity (w.r.t. the length of the input n):
4.86/2.81	
4.86/2.81	   Complexity:  Exp
4.86/2.81	
4.86/2.81	   Cpx degree:  Exp
4.86/2.81	
4.86/2.81	   Solved cost: 2+2^n+n
4.86/2.81	
4.86/2.81	   Rule cost:   2+2^A*B+A
4.86/2.81	
4.86/2.81	   Rule guard:  [ A>=1 && 2^A*B>=1 ]
4.86/2.81	
4.86/2.81	
4.86/2.81	
4.86/2.81	WORST_CASE(EXP,?)
4.86/2.81	
4.86/2.81	
4.86/2.81	----------------------------------------
4.86/2.81	
4.86/2.81	(4)
4.86/2.81	BOUNDS(EXP, INF)
4.86/2.83	EOF