3.24/1.73	MAYBE
3.24/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.24/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.24/1.74	
3.24/1.74	
3.24/1.74	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
3.24/1.74	
3.24/1.74	(0) CpxIntTrs
3.24/1.74	(1) Loat Proof [FINISHED, 13 ms]
3.24/1.74	(2) BOUNDS(1, INF)
3.24/1.74	
3.24/1.74	
3.24/1.74	----------------------------------------
3.24/1.74	
3.24/1.74	(0)
3.24/1.74	Obligation:
3.24/1.74	Complexity Int TRS consisting of the following rules:
3.24/1.74	f(A) -> Com_1(f(A)) :|: 0 >= A * A + 1
3.24/1.74	start(A) -> Com_1(f(A)) :|: TRUE
3.24/1.74	
3.24/1.74	The start-symbols are:[start_1]
3.24/1.74	
3.24/1.74	
3.24/1.74	----------------------------------------
3.24/1.74	
3.24/1.74	(1) Loat Proof (FINISHED)
3.24/1.74	
3.24/1.74	
3.24/1.74	### Pre-processing the ITS problem ###
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	Initial linear ITS problem
3.24/1.74	
3.24/1.74	   Start location: start
3.24/1.74	
3.24/1.74	      0: f -> f : [ 0>=1+A^2 ], cost: 1
3.24/1.74	
3.24/1.74	      1: start -> f : [], cost: 1
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	Removed rules with unsatisfiable guard:
3.24/1.74	
3.24/1.74	   Start location: start
3.24/1.74	
3.24/1.74	      1: start -> f : [], cost: 1
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	### Simplification by acceleration and chaining ###
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	### Computing asymptotic complexity ###
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	Fully simplified ITS problem
3.24/1.74	
3.24/1.74	   Start location: start
3.24/1.74	
3.24/1.74	      1: start -> f : [], cost: 1
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	Obtained the following overall complexity (w.r.t. the length of the input n):
3.24/1.74	
3.24/1.74	   Complexity:  Unknown
3.24/1.74	
3.24/1.74	   Cpx degree:  ?
3.24/1.74	
3.24/1.74	   Solved cost: 0
3.24/1.74	
3.24/1.74	   Rule cost:   0
3.24/1.74	
3.24/1.74	   Rule guard:  []
3.24/1.74	
3.24/1.74	
3.24/1.74	
3.24/1.74	WORST_CASE(Omega(0),?)
3.24/1.74	
3.24/1.74	
3.24/1.74	----------------------------------------
3.24/1.74	
3.24/1.74	(2)
3.24/1.74	BOUNDS(1, INF)
3.24/1.76	EOF