5.14/3.07	MAYBE
5.14/3.07	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.14/3.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.14/3.07	
5.14/3.07	
5.14/3.07	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.14/3.07	
5.14/3.07	(0) CpxIntTrs
5.14/3.07	(1) Loat Proof [FINISHED, 121 ms]
5.14/3.07	(2) BOUNDS(1, INF)
5.14/3.07	
5.14/3.07	
5.14/3.07	----------------------------------------
5.14/3.07	
5.14/3.07	(0)
5.14/3.07	Obligation:
5.14/3.07	Complexity Int TRS consisting of the following rules:
5.14/3.07	f2(A, B, C) -> Com_1(f1(A + B, B, D)) :|: 0 >= 1 + A + B
5.14/3.07	f2(A, B, C) -> Com_1(f2(A + B, B, C)) :|: A + B >= 0
5.14/3.07	f300(A, B, C) -> Com_1(f2(A, B, C)) :|: TRUE
5.14/3.07	
5.14/3.07	The start-symbols are:[f300_3]
5.14/3.07	
5.14/3.07	
5.14/3.07	----------------------------------------
5.14/3.07	
5.14/3.07	(1) Loat Proof (FINISHED)
5.14/3.07	
5.14/3.07	
5.14/3.07	### Pre-processing the ITS problem ###
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Initial linear ITS problem
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	      0: f2 -> f1 : A'=A+B, C'=free, [ 0>=1+A+B ], cost: 1
5.14/3.07	
5.14/3.07	      1: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.14/3.07	
5.14/3.07	      2: f300 -> f2 : [], cost: 1
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Removed unreachable and leaf rules:
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	      1: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.14/3.07	
5.14/3.07	      2: f300 -> f2 : [], cost: 1
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	### Simplification by acceleration and chaining ###
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Accelerating simple loops of location 0.
5.14/3.07	
5.14/3.07	   Accelerating the following rules:
5.14/3.07	
5.14/3.07	      1: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	   Found no metering function for rule 1.
5.14/3.07	
5.14/3.07	   Removing the simple loops:.
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Accelerated all simple loops using metering functions (where possible):
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	      1: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.14/3.07	
5.14/3.07	      2: f300 -> f2 : [], cost: 1
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Chained accelerated rules (with incoming rules):
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	      2: f300 -> f2 : [], cost: 1
5.14/3.07	
5.14/3.07	      3: f300 -> f2 : A'=A+B, [ A+B>=0 ], cost: 2
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Removed unreachable locations (and leaf rules with constant cost):
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	### Computing asymptotic complexity ###
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Fully simplified ITS problem
5.14/3.07	
5.14/3.07	   Start location: f300
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	Obtained the following overall complexity (w.r.t. the length of the input n):
5.14/3.07	
5.14/3.07	   Complexity:  Unknown
5.14/3.07	
5.14/3.07	   Cpx degree:  ?
5.14/3.07	
5.14/3.07	   Solved cost: 0
5.14/3.07	
5.14/3.07	   Rule cost:   0
5.14/3.07	
5.14/3.07	   Rule guard:  []
5.14/3.07	
5.14/3.07	
5.14/3.07	
5.14/3.07	WORST_CASE(Omega(0),?)
5.14/3.07	
5.14/3.07	
5.14/3.07	----------------------------------------
5.14/3.07	
5.14/3.07	(2)
5.14/3.07	BOUNDS(1, INF)
5.14/3.10	EOF