3.42/1.79	WORST_CASE(NON_POLY, ?)
3.42/1.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.42/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.42/1.80	
3.42/1.80	
3.42/1.80	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.42/1.80	
3.42/1.80	(0) CpxIntTrs
3.42/1.80	(1) Loat Proof [FINISHED, 114 ms]
3.42/1.80	(2) BOUNDS(INF, INF)
3.42/1.80	
3.42/1.80	
3.42/1.80	----------------------------------------
3.42/1.80	
3.42/1.80	(0)
3.42/1.80	Obligation:
3.42/1.80	Complexity Int TRS consisting of the following rules:
3.42/1.80	f3(A, B) -> Com_1(f2(A, B)) :|: TRUE
3.42/1.80	f2(A, B) -> Com_1(f2(-(1) + A, B)) :|: 1 >= A
3.42/1.80	f2(A, B) -> Com_1(f300(-(1) + A, C)) :|: A >= 2
3.42/1.80	
3.42/1.80	The start-symbols are:[f3_2]
3.42/1.80	
3.42/1.80	
3.42/1.80	----------------------------------------
3.42/1.80	
3.42/1.80	(1) Loat Proof (FINISHED)
3.42/1.80	
3.42/1.80	
3.42/1.80	### Pre-processing the ITS problem ###
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Initial linear ITS problem
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      0: f3 -> f2 : [], cost: 1
3.42/1.80	
3.42/1.80	      1: f2 -> f2 : A'=-1+A, [ 1>=A ], cost: 1
3.42/1.80	
3.42/1.80	      2: f2 -> f300 : A'=-1+A, B'=free, [ A>=2 ], cost: 1
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Removed unreachable and leaf rules:
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      0: f3 -> f2 : [], cost: 1
3.42/1.80	
3.42/1.80	      1: f2 -> f2 : A'=-1+A, [ 1>=A ], cost: 1
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	### Simplification by acceleration and chaining ###
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Accelerating simple loops of location 1.
3.42/1.80	
3.42/1.80	   Accelerating the following rules:
3.42/1.80	
3.42/1.80	      1: f2 -> f2 : A'=-1+A, [ 1>=A ], cost: 1
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	   Accelerated rule 1 with NONTERM, yielding the new rule 3.
3.42/1.80	
3.42/1.80	   Removing the simple loops: 1.
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Accelerated all simple loops using metering functions (where possible):
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      0: f3 -> f2 : [], cost: 1
3.42/1.80	
3.42/1.80	      3: f2 -> [3] : [ 1>=A ], cost: INF
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Chained accelerated rules (with incoming rules):
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      0: f3 -> f2 : [], cost: 1
3.42/1.80	
3.42/1.80	      4: f3 -> [3] : [ 1>=A ], cost: INF
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Removed unreachable locations (and leaf rules with constant cost):
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      4: f3 -> [3] : [ 1>=A ], cost: INF
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	### Computing asymptotic complexity ###
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Fully simplified ITS problem
3.42/1.80	
3.42/1.80	   Start location: f3
3.42/1.80	
3.42/1.80	      4: f3 -> [3] : [ 1>=A ], cost: INF
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Computing asymptotic complexity for rule 4
3.42/1.80	
3.42/1.80	   Resulting cost INF has complexity: Nonterm
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Found new complexity Nonterm.
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	Obtained the following overall complexity (w.r.t. the length of the input n):
3.42/1.80	
3.42/1.80	   Complexity:  Nonterm
3.42/1.80	
3.42/1.80	   Cpx degree:  Nonterm
3.42/1.80	
3.42/1.80	   Solved cost: INF
3.42/1.80	
3.42/1.80	   Rule cost:   INF
3.42/1.80	
3.42/1.80	   Rule guard:  [ 1>=A ]
3.42/1.80	
3.42/1.80	
3.42/1.80	
3.42/1.80	NO
3.42/1.80	
3.42/1.80	
3.42/1.80	----------------------------------------
3.42/1.80	
3.42/1.80	(2)
3.42/1.80	BOUNDS(INF, INF)
3.86/1.82	EOF