5.41/2.95	MAYBE
5.41/2.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.41/2.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.41/2.96	
5.41/2.96	
5.41/2.96	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.41/2.96	
5.41/2.96	(0) CpxIntTrs
5.41/2.96	(1) Loat Proof [FINISHED, 299 ms]
5.41/2.96	(2) BOUNDS(1, INF)
5.41/2.96	
5.41/2.96	
5.41/2.96	----------------------------------------
5.41/2.96	
5.41/2.96	(0)
5.41/2.96	Obligation:
5.41/2.96	Complexity Int TRS consisting of the following rules:
5.41/2.96	f0(A, B, C, D, E, F) -> Com_1(f0(-(1) + A, C, -(1) + C, A, E, F)) :|: A >= 1
5.41/2.96	f1(A, B, C, D, E, F) -> Com_1(f0(-(1) + A, B, -(1) + C, D, C, A)) :|: A >= 1 && C >= 1
5.41/2.96	f0(A, B, C, D, E, F) -> Com_1(f0(5000, B, C, D, E, F)) :|: 0 >= A && C >= 1
5.41/2.96	f3(A, B, C, D, E, F) -> Com_1(f0(5000, B, G, D, E, F)) :|: G >= 1
5.41/2.96	
5.41/2.96	The start-symbols are:[f3_6]
5.41/2.96	
5.41/2.96	
5.41/2.96	----------------------------------------
5.41/2.96	
5.41/2.96	(1) Loat Proof (FINISHED)
5.41/2.96	
5.41/2.96	
5.41/2.96	### Pre-processing the ITS problem ###
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Initial linear ITS problem
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	      0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      1: f1 -> f0 : A'=-1+A, C'=-1+C, E'=C, F'=A, [ A>=1 && C>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Removed unreachable and leaf rules:
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	      0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	### Simplification by acceleration and chaining ###
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Accelerating simple loops of location 0.
5.41/2.96	
5.41/2.96	   Accelerating the following rules:
5.41/2.96	
5.41/2.96	      0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	   Accelerated rule 0 with metering function A, yielding the new rule 4.
5.41/2.96	
5.41/2.96	   Found no metering function for rule 2.
5.41/2.96	
5.41/2.96	   Removing the simple loops: 0.
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Accelerated all simple loops using metering functions (where possible):
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	      2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      4: f0 -> f0 : A'=0, B'=1+C-A, C'=C-A, D'=1, [ A>=1 ], cost: A
5.41/2.96	
5.41/2.96	      3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Chained accelerated rules (with incoming rules):
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	      3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1
5.41/2.96	
5.41/2.96	      5: f3 -> f0 : A'=0, B'=-4999+free, C'=-5000+free, D'=1, [ free>=1 ], cost: 5001
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Removed unreachable locations (and leaf rules with constant cost):
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	### Computing asymptotic complexity ###
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Fully simplified ITS problem
5.41/2.96	
5.41/2.96	   Start location: f3
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	Obtained the following overall complexity (w.r.t. the length of the input n):
5.41/2.96	
5.41/2.96	   Complexity:  Unknown
5.41/2.96	
5.41/2.96	   Cpx degree:  ?
5.41/2.96	
5.41/2.96	   Solved cost: 0
5.41/2.96	
5.41/2.96	   Rule cost:   0
5.41/2.96	
5.41/2.96	   Rule guard:  []
5.41/2.96	
5.41/2.96	
5.41/2.96	
5.41/2.96	WORST_CASE(Omega(0),?)
5.41/2.96	
5.41/2.96	
5.41/2.96	----------------------------------------
5.41/2.96	
5.41/2.96	(2)
5.41/2.96	BOUNDS(1, INF)
5.51/2.98	EOF