4.91/2.78	MAYBE
4.91/2.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.91/2.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.91/2.79	
4.91/2.79	
4.91/2.79	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
4.91/2.79	
4.91/2.79	(0) CpxIntTrs
4.91/2.79	(1) Loat Proof [FINISHED, 112 ms]
4.91/2.79	(2) BOUNDS(1, INF)
4.91/2.79	
4.91/2.79	
4.91/2.79	----------------------------------------
4.91/2.79	
4.91/2.79	(0)
4.91/2.79	Obligation:
4.91/2.79	Complexity Int TRS consisting of the following rules:
4.91/2.79	f1(A, B) -> Com_1(f2(A, B)) :|: 0 >= A + B + 1 && A >= 1
4.91/2.79	f2(A, B) -> Com_1(f2(A - B, B)) :|: A >= 0
4.91/2.79	f2(A, B) -> Com_1(f3(A, B)) :|: 0 >= A + 1
4.91/2.79	
4.91/2.79	The start-symbols are:[f1_2]
4.91/2.79	
4.91/2.79	
4.91/2.79	----------------------------------------
4.91/2.79	
4.91/2.79	(1) Loat Proof (FINISHED)
4.91/2.79	
4.91/2.79	
4.91/2.79	### Pre-processing the ITS problem ###
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Initial linear ITS problem
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	      0: f1 -> f2 : [ 0>=1+A+B && A>=1 ], cost: 1
4.91/2.79	
4.91/2.79	      1: f2 -> f2 : A'=A-B, [ A>=0 ], cost: 1
4.91/2.79	
4.91/2.79	      2: f2 -> f3 : [ 0>=1+A ], cost: 1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Removed unreachable and leaf rules:
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	      0: f1 -> f2 : [ 0>=1+A+B && A>=1 ], cost: 1
4.91/2.79	
4.91/2.79	      1: f2 -> f2 : A'=A-B, [ A>=0 ], cost: 1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	### Simplification by acceleration and chaining ###
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Accelerating simple loops of location 1.
4.91/2.79	
4.91/2.79	   Accelerating the following rules:
4.91/2.79	
4.91/2.79	      1: f2 -> f2 : A'=A-B, [ A>=0 ], cost: 1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	   Found no metering function for rule 1.
4.91/2.79	
4.91/2.79	   Removing the simple loops:.
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Accelerated all simple loops using metering functions (where possible):
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	      0: f1 -> f2 : [ 0>=1+A+B && A>=1 ], cost: 1
4.91/2.79	
4.91/2.79	      1: f2 -> f2 : A'=A-B, [ A>=0 ], cost: 1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Chained accelerated rules (with incoming rules):
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	      0: f1 -> f2 : [ 0>=1+A+B && A>=1 ], cost: 1
4.91/2.79	
4.91/2.79	      3: f1 -> f2 : A'=A-B, [ 0>=1+A+B && A>=1 ], cost: 2
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Removed unreachable locations (and leaf rules with constant cost):
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	### Computing asymptotic complexity ###
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Fully simplified ITS problem
4.91/2.79	
4.91/2.79	   Start location: f1
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	Obtained the following overall complexity (w.r.t. the length of the input n):
4.91/2.79	
4.91/2.79	   Complexity:  Unknown
4.91/2.79	
4.91/2.79	   Cpx degree:  ?
4.91/2.79	
4.91/2.79	   Solved cost: 0
4.91/2.79	
4.91/2.79	   Rule cost:   0
4.91/2.79	
4.91/2.79	   Rule guard:  []
4.91/2.79	
4.91/2.79	
4.91/2.79	
4.91/2.79	WORST_CASE(Omega(0),?)
4.91/2.79	
4.91/2.79	
4.91/2.79	----------------------------------------
4.91/2.79	
4.91/2.79	(2)
4.91/2.79	BOUNDS(1, INF)
4.97/2.82	EOF