3.38/1.93	WORST_CASE(NON_POLY, ?)
3.38/1.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.38/1.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.38/1.93	
3.38/1.93	
3.38/1.93	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.38/1.93	
3.38/1.93	(0) CpxIntTrs
3.38/1.93	(1) Loat Proof [FINISHED, 221 ms]
3.38/1.93	(2) BOUNDS(INF, INF)
3.38/1.93	
3.38/1.93	
3.38/1.93	----------------------------------------
3.38/1.93	
3.38/1.93	(0)
3.38/1.93	Obligation:
3.38/1.93	Complexity Int TRS consisting of the following rules:
3.38/1.93	f3(A) -> Com_1(f2(A)) :|: TRUE
3.38/1.93	f2(A) -> Com_1(f2(-(1) + A)) :|: A >= 2
3.38/1.93	f2(A) -> Com_1(f2(-(1) + A)) :|: 1 >= A
3.38/1.93	
3.38/1.93	The start-symbols are:[f3_1]
3.38/1.93	
3.38/1.93	
3.38/1.93	----------------------------------------
3.38/1.93	
3.38/1.93	(1) Loat Proof (FINISHED)
3.38/1.93	
3.38/1.93	
3.38/1.93	### Pre-processing the ITS problem ###
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Initial linear ITS problem
3.38/1.93	
3.38/1.93	   Start location: f3
3.38/1.93	
3.38/1.93	      0: f3 -> f2 : [], cost: 1
3.38/1.93	
3.38/1.93	      1: f2 -> f2 : A'=-1+A, [ A>=2 ], cost: 1
3.38/1.93	
3.38/1.93	      2: f2 -> f2 : A'=-1+A, [ 1>=A ], cost: 1
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	### Simplification by acceleration and chaining ###
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Accelerating simple loops of location 1.
3.38/1.93	
3.38/1.93	   Accelerating the following rules:
3.38/1.93	
3.38/1.93	      1: f2 -> f2 : A'=-1+A, [ A>=2 ], cost: 1
3.38/1.93	
3.38/1.93	      2: f2 -> f2 : A'=-1+A, [ 1>=A ], cost: 1
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	   Accelerated rule 1 with metering function -1+A, yielding the new rule 3.
3.38/1.93	
3.38/1.93	   Accelerated rule 2 with NONTERM, yielding the new rule 4.
3.38/1.93	
3.38/1.93	   Removing the simple loops: 1 2.
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Accelerated all simple loops using metering functions (where possible):
3.38/1.93	
3.38/1.93	   Start location: f3
3.38/1.93	
3.38/1.93	      0: f3 -> f2 : [], cost: 1
3.38/1.93	
3.38/1.93	      3: f2 -> f2 : A'=1, [ A>=2 ], cost: -1+A
3.38/1.93	
3.38/1.93	      4: f2 -> [2] : [ 1>=A ], cost: INF
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Chained accelerated rules (with incoming rules):
3.38/1.93	
3.38/1.93	   Start location: f3
3.38/1.93	
3.38/1.93	      0: f3 -> f2 : [], cost: 1
3.38/1.93	
3.38/1.93	      5: f3 -> f2 : A'=1, [ A>=2 ], cost: A
3.38/1.93	
3.38/1.93	      6: f3 -> [2] : [ 1>=A ], cost: INF
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Removed unreachable locations (and leaf rules with constant cost):
3.38/1.93	
3.38/1.93	   Start location: f3
3.38/1.93	
3.38/1.93	      5: f3 -> f2 : A'=1, [ A>=2 ], cost: A
3.38/1.93	
3.38/1.93	      6: f3 -> [2] : [ 1>=A ], cost: INF
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	### Computing asymptotic complexity ###
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Fully simplified ITS problem
3.38/1.93	
3.38/1.93	   Start location: f3
3.38/1.93	
3.38/1.93	      5: f3 -> f2 : A'=1, [ A>=2 ], cost: A
3.38/1.93	
3.38/1.93	      6: f3 -> [2] : [ 1>=A ], cost: INF
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Computing asymptotic complexity for rule 5
3.38/1.93	
3.38/1.93	   Solved the limit problem by the following transformations:
3.38/1.93	
3.38/1.93	      Created initial limit problem:
3.38/1.93	
3.38/1.93	      -1+A (+/+!), A (+) [not solved]
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	      removing all constraints (solved by SMT)
3.38/1.93	
3.38/1.93	      resulting limit problem: [solved]
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	      applying transformation rule (C) using substitution {A==n}
3.38/1.93	
3.38/1.93	      resulting limit problem:
3.38/1.93	
3.38/1.93	      [solved]
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	   Solution:
3.38/1.93	
3.38/1.93	      A / n
3.38/1.93	
3.38/1.93	   Resulting cost n has complexity: Poly(n^1)
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Found new complexity Poly(n^1).
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Computing asymptotic complexity for rule 6
3.38/1.93	
3.38/1.93	   Resulting cost INF has complexity: Nonterm
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Found new complexity Nonterm.
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	Obtained the following overall complexity (w.r.t. the length of the input n):
3.38/1.93	
3.38/1.93	   Complexity:  Nonterm
3.38/1.93	
3.38/1.93	   Cpx degree:  Nonterm
3.38/1.93	
3.38/1.93	   Solved cost: INF
3.38/1.93	
3.38/1.93	   Rule cost:   INF
3.38/1.93	
3.38/1.93	   Rule guard:  [ 1>=A ]
3.38/1.93	
3.38/1.93	
3.38/1.93	
3.38/1.93	NO
3.38/1.93	
3.38/1.93	
3.38/1.93	----------------------------------------
3.38/1.93	
3.38/1.93	(2)
3.38/1.93	BOUNDS(INF, INF)
3.38/1.96	EOF