3.82/1.85	WORST_CASE(NON_POLY, ?)
3.82/1.86	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.82/1.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.82/1.86	
3.82/1.86	
3.82/1.86	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.82/1.86	
3.82/1.86	(0) CpxIntTrs
3.82/1.86	(1) Loat Proof [FINISHED, 133 ms]
3.82/1.86	(2) BOUNDS(INF, INF)
3.82/1.86	
3.82/1.86	
3.82/1.86	----------------------------------------
3.82/1.86	
3.82/1.86	(0)
3.82/1.86	Obligation:
3.82/1.86	Complexity Int TRS consisting of the following rules:
3.82/1.86	f0(A) -> Com_1(f3(A)) :|: TRUE
3.82/1.86	f3(A) -> Com_1(f3(A - 1)) :|: A >= 2
3.82/1.86	f3(A) -> Com_1(f3(A - 1)) :|: TRUE
3.82/1.86	
3.82/1.86	The start-symbols are:[f0_1]
3.82/1.86	
3.82/1.86	
3.82/1.86	----------------------------------------
3.82/1.86	
3.82/1.86	(1) Loat Proof (FINISHED)
3.82/1.86	
3.82/1.86	
3.82/1.86	### Pre-processing the ITS problem ###
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Initial linear ITS problem
3.82/1.86	
3.82/1.86	   Start location: f0
3.82/1.86	
3.82/1.86	      0: f0 -> f3 : [], cost: 1
3.82/1.86	
3.82/1.86	      1: f3 -> f3 : A'=-1+A, [ A>=2 ], cost: 1
3.82/1.86	
3.82/1.86	      2: f3 -> f3 : A'=-1+A, [], cost: 1
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	### Simplification by acceleration and chaining ###
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Accelerating simple loops of location 1.
3.82/1.86	
3.82/1.86	   Accelerating the following rules:
3.82/1.86	
3.82/1.86	      1: f3 -> f3 : A'=-1+A, [ A>=2 ], cost: 1
3.82/1.86	
3.82/1.86	      2: f3 -> f3 : A'=-1+A, [], cost: 1
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	   Accelerated rule 1 with metering function -1+A, yielding the new rule 3.
3.82/1.86	
3.82/1.86	   Accelerated rule 2 with NONTERM, yielding the new rule 4.
3.82/1.86	
3.82/1.86	   Removing the simple loops: 1 2.
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Accelerated all simple loops using metering functions (where possible):
3.82/1.86	
3.82/1.86	   Start location: f0
3.82/1.86	
3.82/1.86	      0: f0 -> f3 : [], cost: 1
3.82/1.86	
3.82/1.86	      3: f3 -> f3 : A'=1, [ A>=2 ], cost: -1+A
3.82/1.86	
3.82/1.86	      4: f3 -> [2] : [], cost: INF
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Chained accelerated rules (with incoming rules):
3.82/1.86	
3.82/1.86	   Start location: f0
3.82/1.86	
3.82/1.86	      0: f0 -> f3 : [], cost: 1
3.82/1.86	
3.82/1.86	      5: f0 -> f3 : A'=1, [ A>=2 ], cost: A
3.82/1.86	
3.82/1.86	      6: f0 -> [2] : [], cost: INF
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Removed unreachable locations (and leaf rules with constant cost):
3.82/1.86	
3.82/1.86	   Start location: f0
3.82/1.86	
3.82/1.86	      5: f0 -> f3 : A'=1, [ A>=2 ], cost: A
3.82/1.86	
3.82/1.86	      6: f0 -> [2] : [], cost: INF
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	### Computing asymptotic complexity ###
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Fully simplified ITS problem
3.82/1.86	
3.82/1.86	   Start location: f0
3.82/1.86	
3.82/1.86	      5: f0 -> f3 : A'=1, [ A>=2 ], cost: A
3.82/1.86	
3.82/1.86	      6: f0 -> [2] : [], cost: INF
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Computing asymptotic complexity for rule 5
3.82/1.86	
3.82/1.86	   Solved the limit problem by the following transformations:
3.82/1.86	
3.82/1.86	      Created initial limit problem:
3.82/1.86	
3.82/1.86	      -1+A (+/+!), A (+) [not solved]
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	      removing all constraints (solved by SMT)
3.82/1.86	
3.82/1.86	      resulting limit problem: [solved]
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	      applying transformation rule (C) using substitution {A==n}
3.82/1.86	
3.82/1.86	      resulting limit problem:
3.82/1.86	
3.82/1.86	      [solved]
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	   Solution:
3.82/1.86	
3.82/1.86	      A / n
3.82/1.86	
3.82/1.86	   Resulting cost n has complexity: Poly(n^1)
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Found new complexity Poly(n^1).
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Computing asymptotic complexity for rule 6
3.82/1.86	
3.82/1.86	   Resulting cost INF has complexity: Nonterm
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Found new complexity Nonterm.
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	Obtained the following overall complexity (w.r.t. the length of the input n):
3.82/1.86	
3.82/1.86	   Complexity:  Nonterm
3.82/1.86	
3.82/1.86	   Cpx degree:  Nonterm
3.82/1.86	
3.82/1.86	   Solved cost: INF
3.82/1.86	
3.82/1.86	   Rule cost:   INF
3.82/1.86	
3.82/1.86	   Rule guard:  []
3.82/1.86	
3.82/1.86	
3.82/1.86	
3.82/1.86	NO
3.82/1.86	
3.82/1.86	
3.82/1.86	----------------------------------------
3.82/1.86	
3.82/1.86	(2)
3.82/1.86	BOUNDS(INF, INF)
3.82/1.88	EOF