6.98/4.71	MAYBE
6.98/4.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.98/4.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.98/4.72	
6.98/4.72	
6.98/4.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.98/4.72	
6.98/4.72	(0) CpxIntTrs
6.98/4.72	(1) Loat Proof [FINISHED, 205 ms]
6.98/4.72	(2) BOUNDS(1, INF)
6.98/4.72	
6.98/4.72	
6.98/4.72	----------------------------------------
6.98/4.72	
6.98/4.72	(0)
6.98/4.72	Obligation:
6.98/4.72	Complexity Int TRS consisting of the following rules:
6.98/4.72	f0(A, B, C) -> Com_1(f1(A, B, C)) :|: TRUE
6.98/4.72	f1(A, B, C) -> Com_1(f1(A + B, B - 1, C)) :|: A >= 1
6.98/4.72	f1(A, B, C) -> Com_1(f1(A + C, B, C - 1)) :|: A >= 1
6.98/4.72	
6.98/4.72	The start-symbols are:[f0_3]
6.98/4.72	
6.98/4.72	
6.98/4.72	----------------------------------------
6.98/4.72	
6.98/4.72	(1) Loat Proof (FINISHED)
6.98/4.72	
6.98/4.72	
6.98/4.72	### Pre-processing the ITS problem ###
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Initial linear ITS problem
6.98/4.72	
6.98/4.72	   Start location: f0
6.98/4.72	
6.98/4.72	      0: f0 -> f1 : [], cost: 1
6.98/4.72	
6.98/4.72	      1: f1 -> f1 : A'=A+B, B'=-1+B, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	      2: f1 -> f1 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	### Simplification by acceleration and chaining ###
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Accelerating simple loops of location 1.
6.98/4.72	
6.98/4.72	   Accelerating the following rules:
6.98/4.72	
6.98/4.72	      1: f1 -> f1 : A'=A+B, B'=-1+B, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	      2: f1 -> f1 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	   Found no metering function for rule 1.
6.98/4.72	
6.98/4.72	   Found no metering function for rule 2.
6.98/4.72	
6.98/4.72	   Removing the simple loops:.
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Accelerated all simple loops using metering functions (where possible):
6.98/4.72	
6.98/4.72	   Start location: f0
6.98/4.72	
6.98/4.72	      0: f0 -> f1 : [], cost: 1
6.98/4.72	
6.98/4.72	      1: f1 -> f1 : A'=A+B, B'=-1+B, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	      2: f1 -> f1 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 1
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Chained accelerated rules (with incoming rules):
6.98/4.72	
6.98/4.72	   Start location: f0
6.98/4.72	
6.98/4.72	      0: f0 -> f1 : [], cost: 1
6.98/4.72	
6.98/4.72	      3: f0 -> f1 : A'=A+B, B'=-1+B, [ A>=1 ], cost: 2
6.98/4.72	
6.98/4.72	      4: f0 -> f1 : A'=C+A, C'=-1+C, [ A>=1 ], cost: 2
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Removed unreachable locations (and leaf rules with constant cost):
6.98/4.72	
6.98/4.72	   Start location: f0
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	### Computing asymptotic complexity ###
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Fully simplified ITS problem
6.98/4.72	
6.98/4.72	   Start location: f0
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	Obtained the following overall complexity (w.r.t. the length of the input n):
6.98/4.72	
6.98/4.72	   Complexity:  Unknown
6.98/4.72	
6.98/4.72	   Cpx degree:  ?
6.98/4.72	
6.98/4.72	   Solved cost: 0
6.98/4.72	
6.98/4.72	   Rule cost:   0
6.98/4.72	
6.98/4.72	   Rule guard:  []
6.98/4.72	
6.98/4.72	
6.98/4.72	
6.98/4.72	WORST_CASE(Omega(0),?)
6.98/4.72	
6.98/4.72	
6.98/4.72	----------------------------------------
6.98/4.72	
6.98/4.72	(2)
6.98/4.72	BOUNDS(1, INF)
6.98/4.76	EOF