3.53/2.01	WORST_CASE(NON_POLY, ?)
3.53/2.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.53/2.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.53/2.02	
3.53/2.02	
3.53/2.02	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(EXP, EXP).
3.53/2.02	
3.53/2.02	(0) CpxIntTrs
3.53/2.02	(1) Koat Proof [FINISHED, 36 ms]
3.53/2.02	(2) BOUNDS(1, EXP)
3.53/2.02	(3) Loat Proof [FINISHED, 337 ms]
3.53/2.02	(4) BOUNDS(EXP, INF)
3.53/2.02	
3.53/2.02	
3.53/2.02	----------------------------------------
3.53/2.02	
3.53/2.02	(0)
3.53/2.02	Obligation:
3.53/2.02	Complexity Int TRS consisting of the following rules:
3.53/2.02	f(A, B, C) -> Com_1(g(A, 1, 0)) :|: TRUE
3.53/2.02	g(A, B, C) -> Com_1(g1(A - 1, B, B)) :|: A > 0
3.53/2.02	g1(A, B, C) -> Com_1(g(A, C + B, C)) :|: TRUE
3.53/2.02	g(A, B, C) -> Com_1(h(A, B, C)) :|: A <= 0
3.53/2.02	h(A, B, C) -> Com_1(h(A, B - 1, C)) :|: B > 0
3.53/2.02	
3.53/2.02	The start-symbols are:[f_3]
3.53/2.02	
3.53/2.02	
3.53/2.02	----------------------------------------
3.53/2.02	
3.53/2.02	(1) Koat Proof (FINISHED)
3.53/2.02	YES(?, pow(2, ar_2) + 2*ar_2 + 2)
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Initial complexity problem:
3.53/2.02	
3.53/2.02	1:	T:
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.53/2.02	
3.53/2.02	2:	T:
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)    f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	A polynomial rank function with
3.53/2.02	
3.53/2.02		Pol(f) = 1
3.53/2.02	
3.53/2.02		Pol(g) = 1
3.53/2.02	
3.53/2.02		Pol(g1) = 1
3.53/2.02	
3.53/2.02		Pol(h) = 0
3.53/2.02	
3.53/2.02		Pol(koat_start) = 1
3.53/2.02	
3.53/2.02	orients all transitions weakly and the transition
3.53/2.02	
3.53/2.02		g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02	strictly and produces the following problem:
3.53/2.02	
3.53/2.02	3:	T:
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)    f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)    h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	A polynomial rank function with
3.53/2.02	
3.53/2.02		Pol(f) = V_3
3.53/2.02	
3.53/2.02		Pol(g) = V_3
3.53/2.02	
3.53/2.02		Pol(g1) = V_3
3.53/2.02	
3.53/2.02		Pol(h) = V_3
3.53/2.02	
3.53/2.02		Pol(koat_start) = V_3
3.53/2.02	
3.53/2.02	orients all transitions weakly and the transition
3.53/2.02	
3.53/2.02		g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02	strictly and produces the following problem:
3.53/2.02	
3.53/2.02	4:	T:
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)       f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ar_2, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)       g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)       g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)       h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Repeatedly propagating knowledge in problem 4 produces the following problem:
3.53/2.02	
3.53/2.02	5:	T:
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)       f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ar_2, Cost: 1)    g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ar_2, Cost: 1)    g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)       g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: ?, Cost: 1)       h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	A polynomial rank function with
3.53/2.02	
3.53/2.02		Pol(h) = V_1
3.53/2.02	
3.53/2.02	and size complexities
3.53/2.02	
3.53/2.02		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
3.53/2.02	
3.53/2.02		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
3.53/2.02	
3.53/2.02		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
3.53/2.02	
3.53/2.02		S("h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-0) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-1) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-0) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-1) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-2) = ar_2
3.53/2.02	
3.53/2.02		S("g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))", 0-0) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))", 0-1) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))", 0-2) = ar_2
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]", 0-0) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]", 0-1) = pow(2, ar_2)
3.53/2.02	
3.53/2.02		S("g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]", 0-2) = ar_2
3.53/2.02	
3.53/2.02		S("f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))", 0-0) = 1
3.53/2.02	
3.53/2.02		S("f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))", 0-1) = 0
3.53/2.02	
3.53/2.02		S("f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))", 0-2) = ar_2
3.53/2.02	
3.53/2.02	orients the transitions
3.53/2.02	
3.53/2.02		h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02	weakly and the transition
3.53/2.02	
3.53/2.02		h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02	strictly and produces the following problem:
3.53/2.02	
3.53/2.02	6:	T:
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)               f(ar_0, ar_1, ar_2) -> Com_1(g(1, 0, ar_2))
3.53/2.02	
3.53/2.02			(Comp: ar_2, Cost: 1)            g(ar_0, ar_1, ar_2) -> Com_1(g1(ar_0, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: ar_2, Cost: 1)            g1(ar_0, ar_1, ar_2) -> Com_1(g(ar_1 + ar_0, ar_1, ar_2))
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 1)               g(ar_0, ar_1, ar_2) -> Com_1(h(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
3.53/2.02	
3.53/2.02			(Comp: pow(2, ar_2), Cost: 1)    h(ar_0, ar_1, ar_2) -> Com_1(h(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= 1 ]
3.53/2.02	
3.53/2.02			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(f(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.53/2.02	
3.53/2.02		start location:	koat_start
3.53/2.02	
3.53/2.02		leaf cost:	0
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Complexity upper bound pow(2, ar_2) + 2*ar_2 + 2
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Time: 0.113 sec (SMT: 0.105 sec)
3.53/2.02	
3.53/2.02	
3.53/2.02	----------------------------------------
3.53/2.02	
3.53/2.02	(2)
3.53/2.02	BOUNDS(1, EXP)
3.53/2.02	
3.53/2.02	----------------------------------------
3.53/2.02	
3.53/2.02	(3) Loat Proof (FINISHED)
3.53/2.02	
3.53/2.02	
3.53/2.02	### Pre-processing the ITS problem ###
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Initial linear ITS problem
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      1: g -> g1 : B'=A, C'=-1+C, [ C>=1 ], cost: 1
3.53/2.02	
3.53/2.02	      3: g -> h : [ 0>=C ], cost: 1
3.53/2.02	
3.53/2.02	      2: g1 -> g : A'=A+B, [], cost: 1
3.53/2.02	
3.53/2.02	      4: h -> h : A'=-1+A, [ A>=1 ], cost: 1
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	### Simplification by acceleration and chaining ###
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Accelerating simple loops of location 3.
3.53/2.02	
3.53/2.02	   Accelerating the following rules:
3.53/2.02	
3.53/2.02	      4: h -> h : A'=-1+A, [ A>=1 ], cost: 1
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	   Accelerated rule 4 with metering function A, yielding the new rule 5.
3.53/2.02	
3.53/2.02	   Removing the simple loops: 4.
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Accelerated all simple loops using metering functions (where possible):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      1: g -> g1 : B'=A, C'=-1+C, [ C>=1 ], cost: 1
3.53/2.02	
3.53/2.02	      3: g -> h : [ 0>=C ], cost: 1
3.53/2.02	
3.53/2.02	      2: g1 -> g : A'=A+B, [], cost: 1
3.53/2.02	
3.53/2.02	      5: h -> h : A'=0, [ A>=1 ], cost: A
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Chained accelerated rules (with incoming rules):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      1: g -> g1 : B'=A, C'=-1+C, [ C>=1 ], cost: 1
3.53/2.02	
3.53/2.02	      3: g -> h : [ 0>=C ], cost: 1
3.53/2.02	
3.53/2.02	      6: g -> h : A'=0, [ 0>=C && A>=1 ], cost: 1+A
3.53/2.02	
3.53/2.02	      2: g1 -> g : A'=A+B, [], cost: 1
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Removed unreachable locations (and leaf rules with constant cost):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      1: g -> g1 : B'=A, C'=-1+C, [ C>=1 ], cost: 1
3.53/2.02	
3.53/2.02	      6: g -> h : A'=0, [ 0>=C && A>=1 ], cost: 1+A
3.53/2.02	
3.53/2.02	      2: g1 -> g : A'=A+B, [], cost: 1
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Eliminated locations (on linear paths):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      6: g -> h : A'=0, [ 0>=C && A>=1 ], cost: 1+A
3.53/2.02	
3.53/2.02	      7: g -> g : A'=2*A, B'=A, C'=-1+C, [ C>=1 ], cost: 2
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Accelerating simple loops of location 1.
3.53/2.02	
3.53/2.02	   Accelerating the following rules:
3.53/2.02	
3.53/2.02	      7: g -> g : A'=2*A, B'=A, C'=-1+C, [ C>=1 ], cost: 2
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	   Accelerated rule 7 with metering function C, yielding the new rule 8.
3.53/2.02	
3.53/2.02	   Removing the simple loops: 7.
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Accelerated all simple loops using metering functions (where possible):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      6: g -> h : A'=0, [ 0>=C && A>=1 ], cost: 1+A
3.53/2.02	
3.53/2.02	      8: g -> g : A'=2^C*A, B'=1/2*2^C*A, C'=0, [ C>=1 ], cost: 2*C
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Chained accelerated rules (with incoming rules):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	      0: f -> g : A'=1, B'=0, [], cost: 1
3.53/2.02	
3.53/2.02	      9: f -> g : A'=2^C, B'=1/2*2^C, C'=0, [ C>=1 ], cost: 1+2*C
3.53/2.02	
3.53/2.02	      6: g -> h : A'=0, [ 0>=C && A>=1 ], cost: 1+A
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Eliminated locations (on tree-shaped paths):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	     10: f -> h : A'=0, B'=0, [ 0>=C ], cost: 3
3.53/2.02	
3.53/2.02	     11: f -> h : A'=0, B'=1/2*2^C, C'=0, [ C>=1 && 2^C>=1 ], cost: 2+2*C+2^C
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Applied pruning (of leafs and parallel rules):
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	     11: f -> h : A'=0, B'=1/2*2^C, C'=0, [ C>=1 && 2^C>=1 ], cost: 2+2*C+2^C
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	### Computing asymptotic complexity ###
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Fully simplified ITS problem
3.53/2.02	
3.53/2.02	   Start location: f
3.53/2.02	
3.53/2.02	     11: f -> h : A'=0, B'=1/2*2^C, C'=0, [ C>=1 && 2^C>=1 ], cost: 2+2*C+2^C
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Computing asymptotic complexity for rule 11
3.53/2.02	
3.53/2.02	   Solved the limit problem by the following transformations:
3.53/2.02	
3.53/2.02	      Created initial limit problem:
3.53/2.02	
3.53/2.02	      2+2*C+2^C (+), C (+/+!), 2^C (+/+!) [not solved]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	      applying transformation rule (E), replacing 2+2*C+2^C (+) by 1 (+/+!) and C (+)
3.53/2.02	
3.53/2.02	      resulting limit problem:
3.53/2.02	
3.53/2.02	      1 (+/+!), C (+), 2^C (+/+!) [not solved]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	      applying transformation rule (B), deleting 1 (+/+!)
3.53/2.02	
3.53/2.02	      resulting limit problem:
3.53/2.02	
3.53/2.02	      C (+), 2^C (+/+!) [not solved]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	      applying transformation rule (E), replacing 2^C (+/+!) by 1 (+/+!) and C (+)
3.53/2.02	
3.53/2.02	      resulting limit problem:
3.53/2.02	
3.53/2.02	      1 (+/+!), C (+) [not solved]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	      applying transformation rule (B), deleting 1 (+/+!)
3.53/2.02	
3.53/2.02	      resulting limit problem:
3.53/2.02	
3.53/2.02	      C (+) [solved]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	   Solution:
3.53/2.02	
3.53/2.02	      C / n
3.53/2.02	
3.53/2.02	   Resulting cost 2+2*n+2^n has complexity: Exp
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Found new complexity Exp.
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	Obtained the following overall complexity (w.r.t. the length of the input n):
3.53/2.02	
3.53/2.02	   Complexity:  Exp
3.53/2.02	
3.53/2.02	   Cpx degree:  Exp
3.53/2.02	
3.53/2.02	   Solved cost: 2+2*n+2^n
3.53/2.02	
3.53/2.02	   Rule cost:   2+2*C+2^C
3.53/2.02	
3.53/2.02	   Rule guard:  [ C>=1 && 2^C>=1 ]
3.53/2.02	
3.53/2.02	
3.53/2.02	
3.53/2.02	WORST_CASE(EXP,?)
3.53/2.02	
3.53/2.02	
3.53/2.02	----------------------------------------
3.53/2.02	
3.53/2.02	(4)
3.53/2.02	BOUNDS(EXP, INF)
4.28/2.15	EOF