3.65/1.80	WORST_CASE(NON_POLY, ?)
3.65/1.80	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.65/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.65/1.80	
3.65/1.80	
3.65/1.80	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.65/1.80	
3.65/1.80	(0) CpxIntTrs
3.65/1.80	(1) Loat Proof [FINISHED, 116 ms]
3.65/1.80	(2) BOUNDS(INF, INF)
3.65/1.80	
3.65/1.80	
3.65/1.80	----------------------------------------
3.65/1.80	
3.65/1.80	(0)
3.65/1.80	Obligation:
3.65/1.80	Complexity Int TRS consisting of the following rules:
3.65/1.80	f0(A) -> Com_1(f2(A + 200)) :|: A + 99 >= 0
3.65/1.80	f0(A) -> Com_1(f2(A + 500)) :|: A >= 1
3.65/1.80	f2(A) -> Com_1(f2(A + 700)) :|: A + 199 >= 0
3.65/1.80	
3.65/1.80	The start-symbols are:[f0_1]
3.65/1.80	
3.65/1.80	
3.65/1.80	----------------------------------------
3.65/1.80	
3.65/1.80	(1) Loat Proof (FINISHED)
3.65/1.80	
3.65/1.80	
3.65/1.80	### Pre-processing the ITS problem ###
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Initial linear ITS problem
3.65/1.80	
3.65/1.80	   Start location: f0
3.65/1.80	
3.65/1.80	      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1
3.65/1.80	
3.65/1.80	      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1
3.65/1.80	
3.65/1.80	      2: f2 -> f2 : A'=700+A, [ 199+A>=0 ], cost: 1
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	### Simplification by acceleration and chaining ###
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Accelerating simple loops of location 1.
3.65/1.80	
3.65/1.80	   Accelerating the following rules:
3.65/1.80	
3.65/1.80	      2: f2 -> f2 : A'=700+A, [ 199+A>=0 ], cost: 1
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	   Accelerated rule 2 with NONTERM, yielding the new rule 3.
3.65/1.80	
3.65/1.80	   Removing the simple loops: 2.
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Accelerated all simple loops using metering functions (where possible):
3.65/1.80	
3.65/1.80	   Start location: f0
3.65/1.80	
3.65/1.80	      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1
3.65/1.80	
3.65/1.80	      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1
3.65/1.80	
3.65/1.80	      3: f2 -> [2] : [ 199+A>=0 ], cost: INF
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Chained accelerated rules (with incoming rules):
3.65/1.80	
3.65/1.80	   Start location: f0
3.65/1.80	
3.65/1.80	      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1
3.65/1.80	
3.65/1.80	      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1
3.65/1.80	
3.65/1.80	      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF
3.65/1.80	
3.65/1.80	      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Removed unreachable locations (and leaf rules with constant cost):
3.65/1.80	
3.65/1.80	   Start location: f0
3.65/1.80	
3.65/1.80	      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF
3.65/1.80	
3.65/1.80	      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	### Computing asymptotic complexity ###
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Fully simplified ITS problem
3.65/1.80	
3.65/1.80	   Start location: f0
3.65/1.80	
3.65/1.80	      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF
3.65/1.80	
3.65/1.80	      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Computing asymptotic complexity for rule 4
3.65/1.80	
3.65/1.80	   Resulting cost INF has complexity: Nonterm
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Found new complexity Nonterm.
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	Obtained the following overall complexity (w.r.t. the length of the input n):
3.65/1.80	
3.65/1.80	   Complexity:  Nonterm
3.65/1.80	
3.65/1.80	   Cpx degree:  Nonterm
3.65/1.80	
3.65/1.80	   Solved cost: INF
3.65/1.80	
3.65/1.80	   Rule cost:   INF
3.65/1.80	
3.65/1.80	   Rule guard:  [ 99+A>=0 ]
3.65/1.80	
3.65/1.80	
3.65/1.80	
3.65/1.80	NO
3.65/1.80	
3.65/1.80	
3.65/1.80	----------------------------------------
3.65/1.80	
3.65/1.80	(2)
3.65/1.80	BOUNDS(INF, INF)
3.81/1.82	EOF