7.14/5.10	MAYBE
7.14/5.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
7.14/5.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.14/5.10	
7.14/5.10	
7.14/5.10	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
7.14/5.10	
7.14/5.10	(0) CpxIntTrs
7.14/5.10	(1) Loat Proof [FINISHED, 124 ms]
7.14/5.10	(2) BOUNDS(1, INF)
7.14/5.10	
7.14/5.10	
7.14/5.10	----------------------------------------
7.14/5.10	
7.14/5.10	(0)
7.14/5.10	Obligation:
7.14/5.10	Complexity Int TRS consisting of the following rules:
7.14/5.10	f0(A, B, C) -> Com_1(f1(A, B, C)) :|: TRUE
7.14/5.10	f1(A, B, C) -> Com_1(f1(A + B, B - C, C + 1)) :|: A >= 1
7.14/5.10	
7.14/5.10	The start-symbols are:[f0_3]
7.14/5.10	
7.14/5.10	
7.14/5.10	----------------------------------------
7.14/5.10	
7.14/5.10	(1) Loat Proof (FINISHED)
7.14/5.10	
7.14/5.10	
7.14/5.10	### Pre-processing the ITS problem ###
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Initial linear ITS problem
7.14/5.10	
7.14/5.10	   Start location: f0
7.14/5.10	
7.14/5.10	      0: f0 -> f1 : [], cost: 1
7.14/5.10	
7.14/5.10	      1: f1 -> f1 : A'=A+B, B'=-C+B, C'=1+C, [ A>=1 ], cost: 1
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	### Simplification by acceleration and chaining ###
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Accelerating simple loops of location 1.
7.14/5.10	
7.14/5.10	   Accelerating the following rules:
7.14/5.10	
7.14/5.10	      1: f1 -> f1 : A'=A+B, B'=-C+B, C'=1+C, [ A>=1 ], cost: 1
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	   Found no metering function for rule 1.
7.14/5.10	
7.14/5.10	   Removing the simple loops:.
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Accelerated all simple loops using metering functions (where possible):
7.14/5.10	
7.14/5.10	   Start location: f0
7.14/5.10	
7.14/5.10	      0: f0 -> f1 : [], cost: 1
7.14/5.10	
7.14/5.10	      1: f1 -> f1 : A'=A+B, B'=-C+B, C'=1+C, [ A>=1 ], cost: 1
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Chained accelerated rules (with incoming rules):
7.14/5.10	
7.14/5.10	   Start location: f0
7.14/5.10	
7.14/5.10	      0: f0 -> f1 : [], cost: 1
7.14/5.10	
7.14/5.10	      2: f0 -> f1 : A'=A+B, B'=-C+B, C'=1+C, [ A>=1 ], cost: 2
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Removed unreachable locations (and leaf rules with constant cost):
7.14/5.10	
7.14/5.10	   Start location: f0
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	### Computing asymptotic complexity ###
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Fully simplified ITS problem
7.14/5.10	
7.14/5.10	   Start location: f0
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	Obtained the following overall complexity (w.r.t. the length of the input n):
7.14/5.10	
7.14/5.10	   Complexity:  Unknown
7.14/5.10	
7.14/5.10	   Cpx degree:  ?
7.14/5.10	
7.14/5.10	   Solved cost: 0
7.14/5.10	
7.14/5.10	   Rule cost:   0
7.14/5.10	
7.14/5.10	   Rule guard:  []
7.14/5.10	
7.14/5.10	
7.14/5.10	
7.14/5.10	WORST_CASE(Omega(0),?)
7.14/5.10	
7.14/5.10	
7.14/5.10	----------------------------------------
7.14/5.10	
7.14/5.10	(2)
7.14/5.10	BOUNDS(1, INF)
7.18/5.13	EOF