5.34/3.16	MAYBE
5.34/3.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.34/3.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.34/3.17	
5.34/3.17	
5.34/3.17	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.34/3.17	
5.34/3.17	(0) CpxIntTrs
5.34/3.17	(1) Loat Proof [FINISHED, 115 ms]
5.34/3.17	(2) BOUNDS(1, INF)
5.34/3.17	
5.34/3.17	
5.34/3.17	----------------------------------------
5.34/3.17	
5.34/3.17	(0)
5.34/3.17	Obligation:
5.34/3.17	Complexity Int TRS consisting of the following rules:
5.34/3.17	f2(A, B, C) -> Com_1(f2(A + B, B, C)) :|: A + B >= 0
5.34/3.17	f3(A, B, C) -> Com_1(f2(A, B, C)) :|: TRUE
5.34/3.17	f2(A, B, C) -> Com_1(f300(A + B, B, D)) :|: 0 >= 1 + A + B
5.34/3.17	
5.34/3.17	The start-symbols are:[f3_3]
5.34/3.17	
5.34/3.17	
5.34/3.17	----------------------------------------
5.34/3.17	
5.34/3.17	(1) Loat Proof (FINISHED)
5.34/3.17	
5.34/3.17	
5.34/3.17	### Pre-processing the ITS problem ###
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Initial linear ITS problem
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	      0: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.34/3.17	
5.34/3.17	      2: f2 -> f300 : A'=A+B, C'=free, [ 0>=1+A+B ], cost: 1
5.34/3.17	
5.34/3.17	      1: f3 -> f2 : [], cost: 1
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Removed unreachable and leaf rules:
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	      0: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.34/3.17	
5.34/3.17	      1: f3 -> f2 : [], cost: 1
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	### Simplification by acceleration and chaining ###
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Accelerating simple loops of location 0.
5.34/3.17	
5.34/3.17	   Accelerating the following rules:
5.34/3.17	
5.34/3.17	      0: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	   Found no metering function for rule 0.
5.34/3.17	
5.34/3.17	   Removing the simple loops:.
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Accelerated all simple loops using metering functions (where possible):
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	      0: f2 -> f2 : A'=A+B, [ A+B>=0 ], cost: 1
5.34/3.17	
5.34/3.17	      1: f3 -> f2 : [], cost: 1
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Chained accelerated rules (with incoming rules):
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	      1: f3 -> f2 : [], cost: 1
5.34/3.17	
5.34/3.17	      3: f3 -> f2 : A'=A+B, [ A+B>=0 ], cost: 2
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Removed unreachable locations (and leaf rules with constant cost):
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	### Computing asymptotic complexity ###
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Fully simplified ITS problem
5.34/3.17	
5.34/3.17	   Start location: f3
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	Obtained the following overall complexity (w.r.t. the length of the input n):
5.34/3.17	
5.34/3.17	   Complexity:  Unknown
5.34/3.17	
5.34/3.17	   Cpx degree:  ?
5.34/3.17	
5.34/3.17	   Solved cost: 0
5.34/3.17	
5.34/3.17	   Rule cost:   0
5.34/3.17	
5.34/3.17	   Rule guard:  []
5.34/3.17	
5.34/3.17	
5.34/3.17	
5.34/3.17	WORST_CASE(Omega(0),?)
5.34/3.17	
5.34/3.17	
5.34/3.17	----------------------------------------
5.34/3.17	
5.34/3.17	(2)
5.34/3.17	BOUNDS(1, INF)
5.34/3.20	EOF