5.12/3.12	MAYBE
5.12/3.13	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.12/3.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.12/3.13	
5.12/3.13	
5.12/3.13	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.12/3.13	
5.12/3.13	(0) CpxIntTrs
5.12/3.13	(1) Loat Proof [FINISHED, 114 ms]
5.12/3.13	(2) BOUNDS(1, INF)
5.12/3.13	
5.12/3.13	
5.12/3.13	----------------------------------------
5.12/3.13	
5.12/3.13	(0)
5.12/3.13	Obligation:
5.12/3.13	Complexity Int TRS consisting of the following rules:
5.12/3.13	f0(A, B) -> Com_1(f1(A, B)) :|: TRUE
5.12/3.13	f1(A, B) -> Com_1(f1(A - B, B + 1)) :|: A >= 1
5.12/3.13	
5.12/3.13	The start-symbols are:[f0_2]
5.12/3.13	
5.12/3.13	
5.12/3.13	----------------------------------------
5.12/3.13	
5.12/3.13	(1) Loat Proof (FINISHED)
5.12/3.13	
5.12/3.13	
5.12/3.13	### Pre-processing the ITS problem ###
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Initial linear ITS problem
5.12/3.13	
5.12/3.13	   Start location: f0
5.12/3.13	
5.12/3.13	      0: f0 -> f1 : [], cost: 1
5.12/3.13	
5.12/3.13	      1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	### Simplification by acceleration and chaining ###
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Accelerating simple loops of location 1.
5.12/3.13	
5.12/3.13	   Accelerating the following rules:
5.12/3.13	
5.12/3.13	      1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	   Found no metering function for rule 1.
5.12/3.13	
5.12/3.13	   Removing the simple loops:.
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Accelerated all simple loops using metering functions (where possible):
5.12/3.13	
5.12/3.13	   Start location: f0
5.12/3.13	
5.12/3.13	      0: f0 -> f1 : [], cost: 1
5.12/3.13	
5.12/3.13	      1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Chained accelerated rules (with incoming rules):
5.12/3.13	
5.12/3.13	   Start location: f0
5.12/3.13	
5.12/3.13	      0: f0 -> f1 : [], cost: 1
5.12/3.13	
5.12/3.13	      2: f0 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 2
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Removed unreachable locations (and leaf rules with constant cost):
5.12/3.13	
5.12/3.13	   Start location: f0
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	### Computing asymptotic complexity ###
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Fully simplified ITS problem
5.12/3.13	
5.12/3.13	   Start location: f0
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	Obtained the following overall complexity (w.r.t. the length of the input n):
5.12/3.13	
5.12/3.13	   Complexity:  Unknown
5.12/3.13	
5.12/3.13	   Cpx degree:  ?
5.12/3.13	
5.12/3.13	   Solved cost: 0
5.12/3.13	
5.12/3.13	   Rule cost:   0
5.12/3.13	
5.12/3.13	   Rule guard:  []
5.12/3.13	
5.12/3.13	
5.12/3.13	
5.12/3.13	WORST_CASE(Omega(0),?)
5.12/3.13	
5.12/3.13	
5.12/3.13	----------------------------------------
5.12/3.13	
5.12/3.13	(2)
5.12/3.13	BOUNDS(1, INF)
5.12/3.15	EOF