6.05/3.77	MAYBE
6.05/3.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.05/3.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.05/3.77	
6.05/3.77	
6.05/3.77	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.05/3.77	
6.05/3.77	(0) CpxIntTrs
6.05/3.77	(1) Loat Proof [FINISHED, 135 ms]
6.05/3.77	(2) BOUNDS(1, INF)
6.05/3.77	
6.05/3.77	
6.05/3.77	----------------------------------------
6.05/3.77	
6.05/3.77	(0)
6.05/3.77	Obligation:
6.05/3.77	Complexity Int TRS consisting of the following rules:
6.05/3.77	f0(A, B, C) -> Com_1(f2(A, D, C)) :|: 0 >= A
6.05/3.77	f0(A, B, C) -> Com_1(f0(A + C, B, -(1) + C)) :|: A >= 1
6.05/3.77	f1(A, B, C) -> Com_1(f0(A, B, C)) :|: TRUE
6.05/3.77	
6.05/3.77	The start-symbols are:[f1_3]
6.05/3.77	
6.05/3.77	
6.05/3.77	----------------------------------------
6.05/3.77	
6.05/3.77	(1) Loat Proof (FINISHED)
6.05/3.77	
6.05/3.77	
6.05/3.77	### Pre-processing the ITS problem ###
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Initial linear ITS problem
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	      0: f0 -> f2 : B'=free, [ 0>=A ], cost: 1
6.05/3.77	
6.05/3.77	      1: f0 -> f0 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.05/3.77	
6.05/3.77	      2: f1 -> f0 : [], cost: 1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Removed unreachable and leaf rules:
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	      1: f0 -> f0 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.05/3.77	
6.05/3.77	      2: f1 -> f0 : [], cost: 1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	### Simplification by acceleration and chaining ###
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Accelerating simple loops of location 0.
6.05/3.77	
6.05/3.77	   Accelerating the following rules:
6.05/3.77	
6.05/3.77	      1: f0 -> f0 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	   Found no metering function for rule 1.
6.05/3.77	
6.05/3.77	   Removing the simple loops:.
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Accelerated all simple loops using metering functions (where possible):
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	      1: f0 -> f0 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.05/3.77	
6.05/3.77	      2: f1 -> f0 : [], cost: 1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Chained accelerated rules (with incoming rules):
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	      2: f1 -> f0 : [], cost: 1
6.05/3.77	
6.05/3.77	      3: f1 -> f0 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 2
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Removed unreachable locations (and leaf rules with constant cost):
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	### Computing asymptotic complexity ###
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Fully simplified ITS problem
6.05/3.77	
6.05/3.77	   Start location: f1
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	Obtained the following overall complexity (w.r.t. the length of the input n):
6.05/3.77	
6.05/3.77	   Complexity:  Unknown
6.05/3.77	
6.05/3.77	   Cpx degree:  ?
6.05/3.77	
6.05/3.77	   Solved cost: 0
6.05/3.77	
6.05/3.77	   Rule cost:   0
6.05/3.77	
6.05/3.77	   Rule guard:  []
6.05/3.77	
6.05/3.77	
6.05/3.77	
6.05/3.77	WORST_CASE(Omega(0),?)
6.05/3.77	
6.05/3.77	
6.05/3.77	----------------------------------------
6.05/3.77	
6.05/3.77	(2)
6.05/3.77	BOUNDS(1, INF)
6.05/3.81	EOF