4.20/2.01	MAYBE
4.20/2.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.20/2.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.20/2.01	
4.20/2.01	
4.20/2.01	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
4.20/2.01	
4.20/2.01	(0) CpxIntTrs
4.20/2.01	(1) Loat Proof [FINISHED, 314 ms]
4.20/2.01	(2) BOUNDS(1, INF)
4.20/2.01	
4.20/2.01	
4.20/2.01	----------------------------------------
4.20/2.01	
4.20/2.01	(0)
4.20/2.01	Obligation:
4.20/2.01	Complexity Int TRS consisting of the following rules:
4.20/2.01	f0(A) -> Com_1(f4(B)) :|: TRUE
4.20/2.01	f4(A) -> Com_1(f4(A + 1)) :|: 3 >= A && A >= 1
4.20/2.01	f4(A) -> Com_1(f4(1)) :|: 0 >= A && 3 >= A
4.20/2.01	f4(A) -> Com_1(f12(A)) :|: A >= 4
4.20/2.01	
4.20/2.01	The start-symbols are:[f0_1]
4.20/2.01	
4.20/2.01	
4.20/2.01	----------------------------------------
4.20/2.01	
4.20/2.01	(1) Loat Proof (FINISHED)
4.20/2.01	
4.20/2.01	
4.20/2.01	### Pre-processing the ITS problem ###
4.20/2.01	
4.20/2.01	
4.20/2.01	
4.20/2.01	Initial linear ITS problem
4.20/2.01	
4.20/2.01	   Start location: f0
4.20/2.01	
4.20/2.01	      0: f0 -> f4 : A'=free, [], cost: 1
4.20/2.01	
4.20/2.01	      1: f4 -> f4 : A'=1+A, [ 3>=A && A>=1 ], cost: 1
4.20/2.01	
4.20/2.01	      2: f4 -> f4 : A'=1, [ 0>=A && 3>=A ], cost: 1
4.20/2.01	
4.20/2.01	      3: f4 -> f12 : [ A>=4 ], cost: 1
4.20/2.01	
4.20/2.01	
4.20/2.01	
4.20/2.01	Removed unreachable and leaf rules:
4.20/2.01	
4.20/2.01	   Start location: f0
4.20/2.02	
4.20/2.02	      0: f0 -> f4 : A'=free, [], cost: 1
4.20/2.02	
4.20/2.02	      1: f4 -> f4 : A'=1+A, [ 3>=A && A>=1 ], cost: 1
4.20/2.02	
4.20/2.02	      2: f4 -> f4 : A'=1, [ 0>=A && 3>=A ], cost: 1
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Simplified all rules, resulting in:
4.20/2.02	
4.20/2.02	   Start location: f0
4.20/2.02	
4.20/2.02	      0: f0 -> f4 : A'=free, [], cost: 1
4.20/2.02	
4.20/2.02	      1: f4 -> f4 : A'=1+A, [ 3>=A && A>=1 ], cost: 1
4.20/2.02	
4.20/2.02	      2: f4 -> f4 : A'=1, [ 0>=A ], cost: 1
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	### Simplification by acceleration and chaining ###
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Accelerating simple loops of location 1.
4.20/2.02	
4.20/2.02	   Accelerating the following rules:
4.20/2.02	
4.20/2.02	      1: f4 -> f4 : A'=1+A, [ 3>=A && A>=1 ], cost: 1
4.20/2.02	
4.20/2.02	      2: f4 -> f4 : A'=1, [ 0>=A ], cost: 1
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	   Accelerated rule 1 with metering function 4-A, yielding the new rule 4.
4.20/2.02	
4.20/2.02	   Found no metering function for rule 2.
4.20/2.02	
4.20/2.02	   Removing the simple loops: 1.
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Accelerated all simple loops using metering functions (where possible):
4.20/2.02	
4.20/2.02	   Start location: f0
4.20/2.02	
4.20/2.02	      0: f0 -> f4 : A'=free, [], cost: 1
4.20/2.02	
4.20/2.02	      2: f4 -> f4 : A'=1, [ 0>=A ], cost: 1
4.20/2.02	
4.20/2.02	      4: f4 -> f4 : A'=4, [ 3>=A && A>=1 ], cost: 4-A
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Chained accelerated rules (with incoming rules):
4.20/2.02	
4.20/2.02	   Start location: f0
4.20/2.02	
4.20/2.02	      0: f0 -> f4 : A'=free, [], cost: 1
4.20/2.02	
4.20/2.02	      5: f0 -> f4 : A'=1, [], cost: 2
4.20/2.02	
4.20/2.02	      6: f0 -> f4 : A'=4, [ 3>=free && free>=1 ], cost: 5-free
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Removed unreachable locations (and leaf rules with constant cost):
4.20/2.02	
4.20/2.02	   Start location: f0
4.20/2.02	
4.20/2.02	      6: f0 -> f4 : A'=4, [ 3>=free && free>=1 ], cost: 5-free
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	### Computing asymptotic complexity ###
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Fully simplified ITS problem
4.20/2.02	
4.20/2.02	   Start location: f0
4.20/2.02	
4.20/2.02	      6: f0 -> f4 : A'=4, [ 3>=free && free>=1 ], cost: 5-free
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Computing asymptotic complexity for rule 6
4.20/2.02	
4.20/2.02	   Could not solve the limit problem.
4.20/2.02	
4.20/2.02	   Resulting cost 0 has complexity: Unknown
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	Obtained the following overall complexity (w.r.t. the length of the input n):
4.20/2.02	
4.20/2.02	   Complexity:  Unknown
4.20/2.02	
4.20/2.02	   Cpx degree:  ?
4.20/2.02	
4.20/2.02	   Solved cost: 0
4.20/2.02	
4.20/2.02	   Rule cost:   0
4.20/2.02	
4.20/2.02	   Rule guard:  []
4.20/2.02	
4.20/2.02	
4.20/2.02	
4.20/2.02	WORST_CASE(Omega(0),?)
4.20/2.02	
4.20/2.02	
4.20/2.02	----------------------------------------
4.20/2.02	
4.20/2.02	(2)
4.20/2.02	BOUNDS(1, INF)
4.23/2.04	EOF