3.92/1.81	WORST_CASE(NON_POLY, ?)
3.92/1.82	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.92/1.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/1.82	
3.92/1.82	
3.92/1.82	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.92/1.82	
3.92/1.82	(0) CpxIntTrs
3.92/1.82	(1) Loat Proof [FINISHED, 134 ms]
3.92/1.82	(2) BOUNDS(INF, INF)
3.92/1.82	
3.92/1.82	
3.92/1.82	----------------------------------------
3.92/1.82	
3.92/1.82	(0)
3.92/1.82	Obligation:
3.92/1.82	Complexity Int TRS consisting of the following rules:
3.92/1.82	f2(A, B) -> Com_1(f2(A, B)) :|: A >= 0
3.92/1.82	f300(A, B) -> Com_1(f2(A, B)) :|: TRUE
3.92/1.82	f2(A, B) -> Com_1(f1(A, C)) :|: 0 >= A + 1
3.92/1.82	
3.92/1.82	The start-symbols are:[f300_2]
3.92/1.82	
3.92/1.82	
3.92/1.82	----------------------------------------
3.92/1.82	
3.92/1.82	(1) Loat Proof (FINISHED)
3.92/1.82	
3.92/1.82	
3.92/1.82	### Pre-processing the ITS problem ###
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Initial linear ITS problem
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      0: f2 -> f2 : [ A>=0 ], cost: 1
3.92/1.82	
3.92/1.82	      2: f2 -> f1 : B'=free, [ 0>=1+A ], cost: 1
3.92/1.82	
3.92/1.82	      1: f300 -> f2 : [], cost: 1
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Removed unreachable and leaf rules:
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      0: f2 -> f2 : [ A>=0 ], cost: 1
3.92/1.82	
3.92/1.82	      1: f300 -> f2 : [], cost: 1
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	### Simplification by acceleration and chaining ###
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Accelerating simple loops of location 0.
3.92/1.82	
3.92/1.82	   Accelerating the following rules:
3.92/1.82	
3.92/1.82	      0: f2 -> f2 : [ A>=0 ], cost: 1
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	   Accelerated rule 0 with NONTERM, yielding the new rule 3.
3.92/1.82	
3.92/1.82	   Removing the simple loops: 0.
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Accelerated all simple loops using metering functions (where possible):
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      3: f2 -> [3] : [ A>=0 ], cost: INF
3.92/1.82	
3.92/1.82	      1: f300 -> f2 : [], cost: 1
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Chained accelerated rules (with incoming rules):
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      1: f300 -> f2 : [], cost: 1
3.92/1.82	
3.92/1.82	      4: f300 -> [3] : [ A>=0 ], cost: INF
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Removed unreachable locations (and leaf rules with constant cost):
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      4: f300 -> [3] : [ A>=0 ], cost: INF
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	### Computing asymptotic complexity ###
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Fully simplified ITS problem
3.92/1.82	
3.92/1.82	   Start location: f300
3.92/1.82	
3.92/1.82	      4: f300 -> [3] : [ A>=0 ], cost: INF
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Computing asymptotic complexity for rule 4
3.92/1.82	
3.92/1.82	   Resulting cost INF has complexity: Nonterm
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Found new complexity Nonterm.
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	Obtained the following overall complexity (w.r.t. the length of the input n):
3.92/1.82	
3.92/1.82	   Complexity:  Nonterm
3.92/1.82	
3.92/1.82	   Cpx degree:  Nonterm
3.92/1.82	
3.92/1.82	   Solved cost: INF
3.92/1.82	
3.92/1.82	   Rule cost:   INF
3.92/1.82	
3.92/1.82	   Rule guard:  [ A>=0 ]
3.92/1.82	
3.92/1.82	
3.92/1.82	
3.92/1.82	NO
3.92/1.82	
3.92/1.82	
3.92/1.82	----------------------------------------
3.92/1.82	
3.92/1.82	(2)
3.92/1.82	BOUNDS(INF, INF)
3.92/1.85	EOF