4.05/1.93	WORST_CASE(NON_POLY, ?)
4.05/1.94	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.05/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.05/1.94	
4.05/1.94	
4.05/1.94	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.05/1.94	
4.05/1.94	(0) CpxIntTrs
4.05/1.94	(1) Loat Proof [FINISHED, 240 ms]
4.05/1.94	(2) BOUNDS(INF, INF)
4.05/1.94	
4.05/1.94	
4.05/1.94	----------------------------------------
4.05/1.94	
4.05/1.94	(0)
4.05/1.94	Obligation:
4.05/1.94	Complexity Int TRS consisting of the following rules:
4.05/1.94	f300(A) -> Com_1(f3(A)) :|: TRUE
4.05/1.94	f3(A) -> Com_1(f3(-(1) + A)) :|: A >= 2
4.05/1.94	f3(A) -> Com_1(f3(-(1) + A)) :|: 1 >= A
4.05/1.94	
4.05/1.94	The start-symbols are:[f300_1]
4.05/1.94	
4.05/1.94	
4.05/1.94	----------------------------------------
4.05/1.94	
4.05/1.94	(1) Loat Proof (FINISHED)
4.05/1.94	
4.05/1.94	
4.05/1.94	### Pre-processing the ITS problem ###
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Initial linear ITS problem
4.05/1.94	
4.05/1.94	   Start location: f300
4.05/1.94	
4.05/1.94	      0: f300 -> f3 : [], cost: 1
4.05/1.94	
4.05/1.94	      1: f3 -> f3 : A'=-1+A, [ A>=2 ], cost: 1
4.05/1.94	
4.05/1.94	      2: f3 -> f3 : A'=-1+A, [ 1>=A ], cost: 1
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	### Simplification by acceleration and chaining ###
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Accelerating simple loops of location 1.
4.05/1.94	
4.05/1.94	   Accelerating the following rules:
4.05/1.94	
4.05/1.94	      1: f3 -> f3 : A'=-1+A, [ A>=2 ], cost: 1
4.05/1.94	
4.05/1.94	      2: f3 -> f3 : A'=-1+A, [ 1>=A ], cost: 1
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	   Accelerated rule 1 with metering function -1+A, yielding the new rule 3.
4.05/1.94	
4.05/1.94	   Accelerated rule 2 with NONTERM, yielding the new rule 4.
4.05/1.94	
4.05/1.94	   Removing the simple loops: 1 2.
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Accelerated all simple loops using metering functions (where possible):
4.05/1.94	
4.05/1.94	   Start location: f300
4.05/1.94	
4.05/1.94	      0: f300 -> f3 : [], cost: 1
4.05/1.94	
4.05/1.94	      3: f3 -> f3 : A'=1, [ A>=2 ], cost: -1+A
4.05/1.94	
4.05/1.94	      4: f3 -> [2] : [ 1>=A ], cost: INF
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Chained accelerated rules (with incoming rules):
4.05/1.94	
4.05/1.94	   Start location: f300
4.05/1.94	
4.05/1.94	      0: f300 -> f3 : [], cost: 1
4.05/1.94	
4.05/1.94	      5: f300 -> f3 : A'=1, [ A>=2 ], cost: A
4.05/1.94	
4.05/1.94	      6: f300 -> [2] : [ 1>=A ], cost: INF
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Removed unreachable locations (and leaf rules with constant cost):
4.05/1.94	
4.05/1.94	   Start location: f300
4.05/1.94	
4.05/1.94	      5: f300 -> f3 : A'=1, [ A>=2 ], cost: A
4.05/1.94	
4.05/1.94	      6: f300 -> [2] : [ 1>=A ], cost: INF
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	### Computing asymptotic complexity ###
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Fully simplified ITS problem
4.05/1.94	
4.05/1.94	   Start location: f300
4.05/1.94	
4.05/1.94	      5: f300 -> f3 : A'=1, [ A>=2 ], cost: A
4.05/1.94	
4.05/1.94	      6: f300 -> [2] : [ 1>=A ], cost: INF
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Computing asymptotic complexity for rule 5
4.05/1.94	
4.05/1.94	   Solved the limit problem by the following transformations:
4.05/1.94	
4.05/1.94	      Created initial limit problem:
4.05/1.94	
4.05/1.94	      -1+A (+/+!), A (+) [not solved]
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	      removing all constraints (solved by SMT)
4.05/1.94	
4.05/1.94	      resulting limit problem: [solved]
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	      applying transformation rule (C) using substitution {A==n}
4.05/1.94	
4.05/1.94	      resulting limit problem:
4.05/1.94	
4.05/1.94	      [solved]
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	   Solution:
4.05/1.94	
4.05/1.94	      A / n
4.05/1.94	
4.05/1.94	   Resulting cost n has complexity: Poly(n^1)
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Found new complexity Poly(n^1).
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Computing asymptotic complexity for rule 6
4.05/1.94	
4.05/1.94	   Resulting cost INF has complexity: Nonterm
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Found new complexity Nonterm.
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	Obtained the following overall complexity (w.r.t. the length of the input n):
4.05/1.94	
4.05/1.94	   Complexity:  Nonterm
4.05/1.94	
4.05/1.94	   Cpx degree:  Nonterm
4.05/1.94	
4.05/1.94	   Solved cost: INF
4.05/1.94	
4.05/1.94	   Rule cost:   INF
4.05/1.94	
4.05/1.94	   Rule guard:  [ 1>=A ]
4.05/1.94	
4.05/1.94	
4.05/1.94	
4.05/1.94	NO
4.05/1.94	
4.05/1.94	
4.05/1.94	----------------------------------------
4.05/1.94	
4.05/1.94	(2)
4.05/1.94	BOUNDS(INF, INF)
4.05/1.97	EOF