3.57/1.97	MAYBE
3.57/1.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.57/1.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.57/1.98	
3.57/1.98	
3.57/1.98	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
3.57/1.98	
3.57/1.98	(0) CpxIntTrs
3.57/1.98	(1) Loat Proof [FINISHED, 208 ms]
3.57/1.98	(2) BOUNDS(1, INF)
3.57/1.98	
3.57/1.98	
3.57/1.98	----------------------------------------
3.57/1.98	
3.57/1.98	(0)
3.57/1.98	Obligation:
3.57/1.98	Complexity Int TRS consisting of the following rules:
3.57/1.98	f0(A, B, C, D) -> Com_1(f6(1, C, C, D)) :|: TRUE
3.57/1.98	f6(A, B, C, D) -> Com_1(f6(A, E, C, E)) :|: B >= A + 2 && E * E >= C + 1
3.57/1.98	f6(A, B, C, D) -> Com_1(f6(E, B, C, E)) :|: B >= A + 2 && C >= E * E
3.57/1.98	f6(A, B, C, D) -> Com_1(f16(A, B, C, D)) :|: A + 1 >= B
3.57/1.98	
3.57/1.98	The start-symbols are:[f0_4]
3.57/1.98	
3.57/1.98	
3.57/1.98	----------------------------------------
3.57/1.98	
3.57/1.98	(1) Loat Proof (FINISHED)
3.57/1.98	
3.57/1.98	
3.57/1.98	### Pre-processing the ITS problem ###
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Initial linear ITS problem
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	      0: f0 -> f6 : A'=1, B'=C, [], cost: 1
3.57/1.98	
3.57/1.98	      1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1
3.57/1.98	
3.57/1.98	      2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1
3.57/1.98	
3.57/1.98	      3: f6 -> f16 : [ 1+A>=B ], cost: 1
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Removed unreachable and leaf rules:
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	      0: f0 -> f6 : A'=1, B'=C, [], cost: 1
3.57/1.98	
3.57/1.98	      1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1
3.57/1.98	
3.57/1.98	      2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	### Simplification by acceleration and chaining ###
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Accelerating simple loops of location 1.
3.57/1.98	
3.57/1.98	   Accelerating the following rules:
3.57/1.98	
3.57/1.98	      1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1
3.57/1.98	
3.57/1.98	      2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	   Found no metering function for rule 1 (rule is too complicated).
3.57/1.98	
3.57/1.98	   Found no metering function for rule 2 (rule is too complicated).
3.57/1.98	
3.57/1.98	   Removing the simple loops:.
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Accelerated all simple loops using metering functions (where possible):
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	      0: f0 -> f6 : A'=1, B'=C, [], cost: 1
3.57/1.98	
3.57/1.98	      1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1
3.57/1.98	
3.57/1.98	      2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Chained accelerated rules (with incoming rules):
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	      0: f0 -> f6 : A'=1, B'=C, [], cost: 1
3.57/1.98	
3.57/1.98	      4: f0 -> f6 : A'=1, B'=free, D'=free, [ C>=3 && free^2>=1+C ], cost: 2
3.57/1.98	
3.57/1.98	      5: f0 -> f6 : A'=free_1, B'=C, D'=free_1, [ C>=3 && C>=free_1^2 ], cost: 2
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Removed unreachable locations (and leaf rules with constant cost):
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	### Computing asymptotic complexity ###
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Fully simplified ITS problem
3.57/1.98	
3.57/1.98	   Start location: f0
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	Obtained the following overall complexity (w.r.t. the length of the input n):
3.57/1.98	
3.57/1.98	   Complexity:  Unknown
3.57/1.98	
3.57/1.98	   Cpx degree:  ?
3.57/1.98	
3.57/1.98	   Solved cost: 0
3.57/1.98	
3.57/1.98	   Rule cost:   0
3.57/1.98	
3.57/1.98	   Rule guard:  []
3.57/1.98	
3.57/1.98	
3.57/1.98	
3.57/1.98	WORST_CASE(Omega(0),?)
3.57/1.98	
3.57/1.98	
3.57/1.98	----------------------------------------
3.57/1.98	
3.57/1.98	(2)
3.57/1.98	BOUNDS(1, INF)
3.85/2.00	EOF