6.83/4.57	MAYBE
6.83/4.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.83/4.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.83/4.58	
6.83/4.58	
6.83/4.58	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.83/4.58	
6.83/4.58	(0) CpxIntTrs
6.83/4.58	(1) Loat Proof [FINISHED, 233 ms]
6.83/4.58	(2) BOUNDS(1, INF)
6.83/4.58	
6.83/4.58	
6.83/4.58	----------------------------------------
6.83/4.58	
6.83/4.58	(0)
6.83/4.58	Obligation:
6.83/4.58	Complexity Int TRS consisting of the following rules:
6.83/4.58	eval(A, B, C) -> Com_1(eval(A + B, B - 2, C + 1)) :|: A >= 0
6.83/4.58	eval(A, B, C) -> Com_1(eval(A + C, B, C - 2)) :|: A >= 0
6.83/4.58	start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE
6.83/4.58	
6.83/4.58	The start-symbols are:[start_3]
6.83/4.58	
6.83/4.58	
6.83/4.58	----------------------------------------
6.83/4.58	
6.83/4.58	(1) Loat Proof (FINISHED)
6.83/4.58	
6.83/4.58	
6.83/4.58	### Pre-processing the ITS problem ###
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Initial linear ITS problem
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	### Simplification by acceleration and chaining ###
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Accelerating simple loops of location 0.
6.83/4.58	
6.83/4.58	   Accelerating the following rules:
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	   Found no metering function for rule 0.
6.83/4.58	
6.83/4.58	   Found no metering function for rule 1.
6.83/4.58	
6.83/4.58	   Removing the simple loops:.
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Accelerated all simple loops using metering functions (where possible):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Chained accelerated rules (with incoming rules):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	      3: start -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 2
6.83/4.58	
6.83/4.58	      4: start -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 2
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Removed unreachable locations (and leaf rules with constant cost):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	### Computing asymptotic complexity ###
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Fully simplified ITS problem
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Obtained the following overall complexity (w.r.t. the length of the input n):
6.83/4.58	
6.83/4.58	   Complexity:  Unknown
6.83/4.58	
6.83/4.58	   Cpx degree:  ?
6.83/4.58	
6.83/4.58	   Solved cost: 0
6.83/4.58	
6.83/4.58	   Rule cost:   0
6.83/4.58	
6.83/4.58	   Rule guard:  []
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	WORST_CASE(Omega(0),?)
6.83/4.58	
6.83/4.58	
6.83/4.58	----------------------------------------
6.83/4.58	
6.83/4.58	(2)
6.83/4.58	BOUNDS(1, INF)
6.88/4.61	EOF