4.67/2.43	WORST_CASE(Omega(n^1), O(n^1))
4.67/2.44	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.67/2.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.67/2.44	
4.67/2.44	
4.67/2.44	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.67/2.44	
4.67/2.44	(0) CpxIntTrs
4.67/2.44	(1) Koat Proof [FINISHED, 87 ms]
4.67/2.44	(2) BOUNDS(1, n^1)
4.67/2.44	(3) Loat Proof [FINISHED, 489 ms]
4.67/2.44	(4) BOUNDS(n^1, INF)
4.67/2.44	
4.67/2.44	
4.67/2.44	----------------------------------------
4.67/2.44	
4.67/2.44	(0)
4.67/2.44	Obligation:
4.67/2.44	Complexity Int TRS consisting of the following rules:
4.67/2.44	f0(A, B, C) -> Com_1(f3(-(A), B, C)) :|: TRUE
4.67/2.44	f3(A, B, C) -> Com_1(f7(0, D, C)) :|: A >= 0 && A <= 0
4.67/2.44	f4(A, B, C) -> Com_1(f7(0, D, C)) :|: A >= 0 && A <= 0
4.67/2.44	f6(A, B, C) -> Com_1(f4(A, B, 1)) :|: A >= 1
4.67/2.44	f3(A, B, C) -> Com_1(f4(-(1) - A, B, 1)) :|: 0 >= A + 1 && 0 >= C
4.67/2.44	f3(A, B, C) -> Com_1(f4(-(1) - A, B, 1)) :|: 0 >= A + 1 && C >= 2
4.67/2.44	f3(A, B, C) -> Com_1(f4(-(1) - A, B, 1)) :|: A >= 1 && 0 >= C
4.67/2.44	f3(A, B, C) -> Com_1(f4(-(1) - A, B, 1)) :|: A >= 1 && C >= 2
4.67/2.44	f4(A, B, C) -> Com_1(f3(1 - A, B, 0)) :|: 0 >= A + 1 && C >= 1 && C <= 1
4.67/2.44	f4(A, B, C) -> Com_1(f3(1 - A, B, 0)) :|: A >= 1 && C >= 1 && C <= 1
4.67/2.44	f5(A, B, C) -> Com_1(f3(1 - A, B, 0)) :|: 0 >= A + 1 && C >= 1 && C <= 1
4.67/2.44	f5(A, B, C) -> Com_1(f3(1 - A, B, 0)) :|: A >= 1 && C >= 1 && C <= 1
4.67/2.44	
4.67/2.44	The start-symbols are:[f6_3]
4.67/2.44	
4.67/2.44	
4.67/2.44	----------------------------------------
4.67/2.44	
4.67/2.44	(1) Koat Proof (FINISHED)
4.67/2.44	YES(?, 2*ar_0 + 3)
4.67/2.44	
4.67/2.44	
4.67/2.44	
4.67/2.44	Initial complexity problem:
4.67/2.44	
4.67/2.44	1:	T:
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0, ar_1, ar_2))
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f6(ar_0, ar_1, ar_2) -> Com_1(f4(ar_0, ar_1, 1)) [ ar_0 >= 1 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ ar_2 >= 2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 /\ ar_2 >= 2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ 0 >= ar_0 + 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f5(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ 0 >= ar_0 + 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f5(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f6(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.67/2.44	
4.67/2.44		start location:	koat_start
4.67/2.44	
4.67/2.44		leaf cost:	0
4.67/2.44	
4.67/2.44	
4.67/2.44	
4.67/2.44	Testing for reachability in the complexity graph removes the following transitions from problem 1:
4.67/2.44	
4.67/2.44		f0(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0, ar_1, ar_2))
4.67/2.44	
4.67/2.44		f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ ar_2 >= 2 ]
4.67/2.44	
4.67/2.44		f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_2 ]
4.67/2.44	
4.67/2.44		f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 /\ ar_2 >= 2 ]
4.67/2.44	
4.67/2.44		f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ 0 >= ar_0 + 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44		f5(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ 0 >= ar_0 + 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44		f5(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44	We thus obtain the following problem:
4.67/2.44	
4.67/2.44	2:	T:
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f6(ar_0, ar_1, ar_2) -> Com_1(f4(ar_0, ar_1, 1)) [ ar_0 >= 1 ]
4.67/2.44	
4.67/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f6(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.67/2.44	
4.67/2.44		start location:	koat_start
4.67/2.44	
4.67/2.44		leaf cost:	0
4.67/2.44	
4.67/2.44	
4.67/2.44	
4.67/2.44	Repeatedly propagating knowledge in problem 2 produces the following problem:
4.67/2.44	
4.67/2.44	3:	T:
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.44	
4.67/2.44			(Comp: 1, Cost: 1)    f6(ar_0, ar_1, ar_2) -> Com_1(f4(ar_0, ar_1, 1)) [ ar_0 >= 1 ]
4.67/2.44	
4.67/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f6(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.67/2.44	
4.67/2.44		start location:	koat_start
4.67/2.44	
4.67/2.44		leaf cost:	0
4.67/2.44	
4.67/2.44	
4.67/2.44	
4.67/2.44	A polynomial rank function with
4.67/2.44	
4.67/2.44		Pol(f4) = 1
4.67/2.44	
4.67/2.44		Pol(f7) = 0
4.67/2.44	
4.67/2.44		Pol(f3) = 1
4.67/2.44	
4.67/2.44		Pol(f6) = 1
4.67/2.44	
4.67/2.44		Pol(koat_start) = 1
4.67/2.44	
4.67/2.44	orients all transitions weakly and the transitions
4.67/2.44	
4.67/2.44		f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44		f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.44	
4.67/2.44	strictly and produces the following problem:
4.67/2.44	
4.67/2.44	4:	T:
4.67/2.44	
4.67/2.44			(Comp: 1, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.45	
4.67/2.45			(Comp: ?, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.45	
4.67/2.45			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 1)    f6(ar_0, ar_1, ar_2) -> Com_1(f4(ar_0, ar_1, 1)) [ ar_0 >= 1 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f6(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.67/2.45	
4.67/2.45		start location:	koat_start
4.67/2.45	
4.67/2.45		leaf cost:	0
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	A polynomial rank function with
4.67/2.45	
4.67/2.45		Pol(f4) = V_1
4.67/2.45	
4.67/2.45		Pol(f7) = 0
4.67/2.45	
4.67/2.45		Pol(f3) = -V_1
4.67/2.45	
4.67/2.45		Pol(f6) = V_1
4.67/2.45	
4.67/2.45		Pol(koat_start) = V_1
4.67/2.45	
4.67/2.45	orients all transitions weakly and the transitions
4.67/2.45	
4.67/2.45		f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.45	
4.67/2.45		f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.45	
4.67/2.45	strictly and produces the following problem:
4.67/2.45	
4.67/2.45	5:	T:
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 1)       f4(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.45	
4.67/2.45			(Comp: ar_0, Cost: 1)    f3(ar_0, ar_1, ar_2) -> Com_1(f4(-ar_0 - 1, ar_1, 1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 1)       f3(ar_0, ar_1, ar_2) -> Com_1(f7(0, d, ar_2)) [ ar_0 = 0 ]
4.67/2.45	
4.67/2.45			(Comp: ar_0, Cost: 1)    f4(ar_0, ar_1, ar_2) -> Com_1(f3(-ar_0 + 1, ar_1, 0)) [ ar_0 >= 1 /\ ar_2 = 1 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 1)       f6(ar_0, ar_1, ar_2) -> Com_1(f4(ar_0, ar_1, 1)) [ ar_0 >= 1 ]
4.67/2.45	
4.67/2.45			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(f6(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.67/2.45	
4.67/2.45		start location:	koat_start
4.67/2.45	
4.67/2.45		leaf cost:	0
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Complexity upper bound 2*ar_0 + 3
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Time: 0.106 sec (SMT: 0.098 sec)
4.67/2.45	
4.67/2.45	
4.67/2.45	----------------------------------------
4.67/2.45	
4.67/2.45	(2)
4.67/2.45	BOUNDS(1, n^1)
4.67/2.45	
4.67/2.45	----------------------------------------
4.67/2.45	
4.67/2.45	(3) Loat Proof (FINISHED)
4.67/2.45	
4.67/2.45	
4.67/2.45	### Pre-processing the ITS problem ###
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Initial linear ITS problem
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	      0: f0 -> f3 : A'=-A, [], cost: 1
4.67/2.45	
4.67/2.45	      1: f3 -> f7 : A'=0, B'=free, [ A==0 ], cost: 1
4.67/2.45	
4.67/2.45	      4: f3 -> f4 : A'=-1-A, C'=1, [ 0>=1+A && 0>=C ], cost: 1
4.67/2.45	
4.67/2.45	      5: f3 -> f4 : A'=-1-A, C'=1, [ 0>=1+A && C>=2 ], cost: 1
4.67/2.45	
4.67/2.45	      6: f3 -> f4 : A'=-1-A, C'=1, [ A>=1 && 0>=C ], cost: 1
4.67/2.45	
4.67/2.45	      7: f3 -> f4 : A'=-1-A, C'=1, [ A>=1 && C>=2 ], cost: 1
4.67/2.45	
4.67/2.45	      2: f4 -> f7 : A'=0, B'=free_1, [ A==0 ], cost: 1
4.67/2.45	
4.67/2.45	      8: f4 -> f3 : A'=1-A, C'=0, [ 0>=1+A && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	      9: f4 -> f3 : A'=1-A, C'=0, [ A>=1 && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	      3: f6 -> f4 : C'=1, [ A>=1 ], cost: 1
4.67/2.45	
4.67/2.45	     10: f5 -> f3 : A'=1-A, C'=0, [ 0>=1+A && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	     11: f5 -> f3 : A'=1-A, C'=0, [ A>=1 && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Removed unreachable and leaf rules:
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	      4: f3 -> f4 : A'=-1-A, C'=1, [ 0>=1+A && 0>=C ], cost: 1
4.67/2.45	
4.67/2.45	      5: f3 -> f4 : A'=-1-A, C'=1, [ 0>=1+A && C>=2 ], cost: 1
4.67/2.45	
4.67/2.45	      6: f3 -> f4 : A'=-1-A, C'=1, [ A>=1 && 0>=C ], cost: 1
4.67/2.45	
4.67/2.45	      7: f3 -> f4 : A'=-1-A, C'=1, [ A>=1 && C>=2 ], cost: 1
4.67/2.45	
4.67/2.45	      8: f4 -> f3 : A'=1-A, C'=0, [ 0>=1+A && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	      9: f4 -> f3 : A'=1-A, C'=0, [ A>=1 && C==1 ], cost: 1
4.67/2.45	
4.67/2.45	      3: f6 -> f4 : C'=1, [ A>=1 ], cost: 1
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	### Simplification by acceleration and chaining ###
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Eliminated locations (on tree-shaped paths):
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	     12: f4 -> f4 : A'=-2+A, C'=1, [ 0>=1+A && C==1 ], cost: 2
4.67/2.45	
4.67/2.45	     13: f4 -> f4 : A'=-2+A, C'=1, [ C==1 && 0>=2-A ], cost: 2
4.67/2.45	
4.67/2.45	      3: f6 -> f4 : C'=1, [ A>=1 ], cost: 1
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Accelerating simple loops of location 2.
4.67/2.45	
4.67/2.45	   Accelerating the following rules:
4.67/2.45	
4.67/2.45	     12: f4 -> f4 : A'=-2+A, C'=1, [ 0>=1+A && C==1 ], cost: 2
4.67/2.45	
4.67/2.45	     13: f4 -> f4 : A'=-2+A, C'=1, [ C==1 && 0>=2-A ], cost: 2
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	   Accelerated rule 12 with NONTERM, yielding the new rule 14.
4.67/2.45	
4.67/2.45	   Accelerated rule 13 with metering function meter (where 2*meter==-1+A), yielding the new rule 15.
4.67/2.45	
4.67/2.45	   Removing the simple loops: 12 13.
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Accelerated all simple loops using metering functions (where possible):
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	     14: f4 -> [6] : [ 0>=1+A && C==1 ], cost: INF
4.67/2.45	
4.67/2.45	     15: f4 -> f4 : A'=A-2*meter, C'=1, [ C==1 && 0>=2-A && 2*meter==-1+A && meter>=1 ], cost: 2*meter
4.67/2.45	
4.67/2.45	      3: f6 -> f4 : C'=1, [ A>=1 ], cost: 1
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Chained accelerated rules (with incoming rules):
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	      3: f6 -> f4 : C'=1, [ A>=1 ], cost: 1
4.67/2.45	
4.67/2.45	     16: f6 -> f4 : A'=A-2*meter, C'=1, [ 0>=2-A && 2*meter==-1+A && meter>=1 ], cost: 1+2*meter
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Removed unreachable locations (and leaf rules with constant cost):
4.67/2.45	
4.67/2.45	   Start location: f6
4.67/2.45	
4.67/2.45	     16: f6 -> f4 : A'=A-2*meter, C'=1, [ 0>=2-A && 2*meter==-1+A && meter>=1 ], cost: 1+2*meter
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	### Computing asymptotic complexity ###
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	Fully simplified ITS problem
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4.67/2.45	   Start location: f6
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4.67/2.45	     16: f6 -> f4 : A'=A-2*meter, C'=1, [ 0>=2-A && 2*meter==-1+A && meter>=1 ], cost: 1+2*meter
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4.67/2.45	
4.67/2.45	Computing asymptotic complexity for rule 16
4.67/2.45	
4.67/2.45	   Solved the limit problem by the following transformations:
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4.67/2.45	      Created initial limit problem:
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4.67/2.45	      -1+A (+/+!), A-2*meter (+/+!), 1+2*meter (+), 2-A+2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (C) using substitution {A==1+2*meter}
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      1 (+/+!), 1+2*meter (+), 2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (B), deleting 1 (+/+!)
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      1+2*meter (+), 2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      removing all constraints (solved by SMT)
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4.67/2.45	      resulting limit problem: [solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (C) using substitution {meter==n}
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      [solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	   Solved the limit problem by the following transformations:
4.67/2.45	
4.67/2.45	      Created initial limit problem:
4.67/2.45	
4.67/2.45	      -1+A (+/+!), A-2*meter (+/+!), 1+2*meter (+), 2-A+2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (C) using substitution {A==1+2*meter}
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      1 (+/+!), 1+2*meter (+), 2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (B), deleting 1 (+/+!)
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      1+2*meter (+), 2*meter (+/+!) [not solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      removing all constraints (solved by SMT)
4.67/2.45	
4.67/2.45	      resulting limit problem: [solved]
4.67/2.45	
4.67/2.45	
4.67/2.45	
4.67/2.45	      applying transformation rule (C) using substitution {meter==n}
4.67/2.45	
4.67/2.45	      resulting limit problem:
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4.67/2.45	      [solved]
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4.67/2.45	
4.67/2.45	   Solution:
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4.67/2.45	      A / 1+2*n
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4.67/2.45	      meter / n
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4.67/2.45	   Resulting cost 1+2*n has complexity: Poly(n^1)
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4.67/2.45	
4.67/2.45	
4.67/2.45	Found new complexity Poly(n^1).
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4.67/2.45	
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4.67/2.45	Obtained the following overall complexity (w.r.t. the length of the input n):
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4.67/2.45	   Complexity:  Poly(n^1)
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4.67/2.45	   Cpx degree:  1
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4.67/2.45	   Solved cost: 1+2*n
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4.67/2.45	   Rule cost:   1+2*meter
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4.67/2.45	   Rule guard:  [ 0>=2-A && 2*meter==-1+A ]
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4.67/2.45	WORST_CASE(Omega(n^1),?)
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4.67/2.45	----------------------------------------
4.67/2.45	
4.67/2.45	(4)
4.67/2.45	BOUNDS(n^1, INF)
4.76/2.48	EOF