10.07/7.86	MAYBE
10.07/7.87	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
10.07/7.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.07/7.87	
10.07/7.87	
10.07/7.87	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
10.07/7.87	
10.07/7.87	(0) CpxIntTrs
10.07/7.87	(1) Loat Proof [FINISHED, 215 ms]
10.07/7.87	(2) BOUNDS(1, INF)
10.07/7.87	
10.07/7.87	
10.07/7.87	----------------------------------------
10.07/7.87	
10.07/7.87	(0)
10.07/7.87	Obligation:
10.07/7.87	Complexity Int TRS consisting of the following rules:
10.07/7.87	f0(A, B, C) -> Com_1(f1(A, B, C)) :|: TRUE
10.07/7.87	f1(A, B, C) -> Com_1(f1(A + 1, B + A + 1, C)) :|: A >= B
10.07/7.87	f1(A, B, C) -> Com_1(f1(A - C, B - 2 * C, C - 1)) :|: A >= B
10.07/7.87	
10.07/7.87	The start-symbols are:[f0_3]
10.07/7.87	
10.07/7.87	
10.07/7.87	----------------------------------------
10.07/7.87	
10.07/7.87	(1) Loat Proof (FINISHED)
10.07/7.87	
10.07/7.87	
10.07/7.87	### Pre-processing the ITS problem ###
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Initial linear ITS problem
10.07/7.87	
10.07/7.87	   Start location: f0
10.07/7.87	
10.07/7.87	      0: f0 -> f1 : [], cost: 1
10.07/7.87	
10.07/7.87	      1: f1 -> f1 : A'=1+A, B'=1+A+B, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	      2: f1 -> f1 : A'=-C+A, B'=-2*C+B, C'=-1+C, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	### Simplification by acceleration and chaining ###
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Accelerating simple loops of location 1.
10.07/7.87	
10.07/7.87	   Accelerating the following rules:
10.07/7.87	
10.07/7.87	      1: f1 -> f1 : A'=1+A, B'=1+A+B, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	      2: f1 -> f1 : A'=-C+A, B'=-2*C+B, C'=-1+C, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	   Found no metering function for rule 1.
10.07/7.87	
10.07/7.87	   Found no metering function for rule 2.
10.07/7.87	
10.07/7.87	   Removing the simple loops:.
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Accelerated all simple loops using metering functions (where possible):
10.07/7.87	
10.07/7.87	   Start location: f0
10.07/7.87	
10.07/7.87	      0: f0 -> f1 : [], cost: 1
10.07/7.87	
10.07/7.87	      1: f1 -> f1 : A'=1+A, B'=1+A+B, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	      2: f1 -> f1 : A'=-C+A, B'=-2*C+B, C'=-1+C, [ A>=B ], cost: 1
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Chained accelerated rules (with incoming rules):
10.07/7.87	
10.07/7.87	   Start location: f0
10.07/7.87	
10.07/7.87	      0: f0 -> f1 : [], cost: 1
10.07/7.87	
10.07/7.87	      3: f0 -> f1 : A'=1+A, B'=1+A+B, [ A>=B ], cost: 2
10.07/7.87	
10.07/7.87	      4: f0 -> f1 : A'=-C+A, B'=-2*C+B, C'=-1+C, [ A>=B ], cost: 2
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Removed unreachable locations (and leaf rules with constant cost):
10.07/7.87	
10.07/7.87	   Start location: f0
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	### Computing asymptotic complexity ###
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Fully simplified ITS problem
10.07/7.87	
10.07/7.87	   Start location: f0
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	Obtained the following overall complexity (w.r.t. the length of the input n):
10.07/7.87	
10.07/7.87	   Complexity:  Unknown
10.07/7.87	
10.07/7.87	   Cpx degree:  ?
10.07/7.87	
10.07/7.87	   Solved cost: 0
10.07/7.87	
10.07/7.87	   Rule cost:   0
10.07/7.87	
10.07/7.87	   Rule guard:  []
10.07/7.87	
10.07/7.87	
10.07/7.87	
10.07/7.87	WORST_CASE(Omega(0),?)
10.07/7.87	
10.07/7.87	
10.07/7.87	----------------------------------------
10.07/7.87	
10.07/7.87	(2)
10.07/7.87	BOUNDS(1, INF)
10.07/7.90	EOF