3.51/2.10	WORST_CASE(NON_POLY, ?)
3.51/2.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.51/2.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.51/2.11	
3.51/2.11	
3.51/2.11	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.51/2.11	
3.51/2.11	(0) CpxIntTrs
3.51/2.11	(1) Loat Proof [FINISHED, 266 ms]
3.51/2.11	(2) BOUNDS(INF, INF)
3.51/2.11	
3.51/2.11	
3.51/2.11	----------------------------------------
3.51/2.11	
3.51/2.11	(0)
3.51/2.11	Obligation:
3.51/2.11	Complexity Int TRS consisting of the following rules:
3.51/2.11	f2(A, B) -> Com_1(f2(-(2) + C, B)) :|: 0 >= A + 1
3.51/2.11	f2(A, B) -> Com_1(f2(2 + C, B)) :|: A >= 1
3.51/2.11	f3(A, B) -> Com_1(f2(A, B)) :|: TRUE
3.51/2.11	f2(A, B) -> Com_1(f300(A, C)) :|: A >= 0 && A <= 0
3.51/2.11	
3.51/2.11	The start-symbols are:[f3_2]
3.51/2.11	
3.51/2.11	
3.51/2.11	----------------------------------------
3.51/2.11	
3.51/2.11	(1) Loat Proof (FINISHED)
3.51/2.11	
3.51/2.11	
3.51/2.11	### Pre-processing the ITS problem ###
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Initial linear ITS problem
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      0: f2 -> f2 : A'=-2+free, [ 0>=1+A ], cost: 1
3.51/2.11	
3.51/2.11	      1: f2 -> f2 : A'=2+free_1, [ A>=1 ], cost: 1
3.51/2.11	
3.51/2.11	      3: f2 -> f300 : B'=free_2, [ A==0 ], cost: 1
3.51/2.11	
3.51/2.11	      2: f3 -> f2 : [], cost: 1
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Removed unreachable and leaf rules:
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      0: f2 -> f2 : A'=-2+free, [ 0>=1+A ], cost: 1
3.51/2.11	
3.51/2.11	      1: f2 -> f2 : A'=2+free_1, [ A>=1 ], cost: 1
3.51/2.11	
3.51/2.11	      2: f3 -> f2 : [], cost: 1
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	### Simplification by acceleration and chaining ###
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Accelerating simple loops of location 0.
3.51/2.11	
3.51/2.11	   Accelerating the following rules:
3.51/2.11	
3.51/2.11	      0: f2 -> f2 : A'=-2+free, [ 0>=1+A ], cost: 1
3.51/2.11	
3.51/2.11	      1: f2 -> f2 : A'=2+free_1, [ A>=1 ], cost: 1
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	   Accelerated rule 0 with NONTERM (after strengthening guard), yielding the new rule 4.
3.51/2.11	
3.51/2.11	   Accelerated rule 1 with NONTERM (after strengthening guard), yielding the new rule 5.
3.51/2.11	
3.51/2.11	   Removing the simple loops:.
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Accelerated all simple loops using metering functions (where possible):
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      0: f2 -> f2 : A'=-2+free, [ 0>=1+A ], cost: 1
3.51/2.11	
3.51/2.11	      1: f2 -> f2 : A'=2+free_1, [ A>=1 ], cost: 1
3.51/2.11	
3.51/2.11	      4: f2 -> [3] : [ 0>=1+A && 0>=-1+free ], cost: INF
3.51/2.11	
3.51/2.11	      5: f2 -> [3] : [ A>=1 && 2+free_1>=1 ], cost: INF
3.51/2.11	
3.51/2.11	      2: f3 -> f2 : [], cost: 1
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Chained accelerated rules (with incoming rules):
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      2: f3 -> f2 : [], cost: 1
3.51/2.11	
3.51/2.11	      6: f3 -> f2 : A'=-2+free, [ 0>=1+A ], cost: 2
3.51/2.11	
3.51/2.11	      7: f3 -> f2 : A'=2+free_1, [ A>=1 ], cost: 2
3.51/2.11	
3.51/2.11	      8: f3 -> [3] : [ 0>=1+A ], cost: INF
3.51/2.11	
3.51/2.11	      9: f3 -> [3] : [ A>=1 ], cost: INF
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Removed unreachable locations (and leaf rules with constant cost):
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      8: f3 -> [3] : [ 0>=1+A ], cost: INF
3.51/2.11	
3.51/2.11	      9: f3 -> [3] : [ A>=1 ], cost: INF
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	### Computing asymptotic complexity ###
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Fully simplified ITS problem
3.51/2.11	
3.51/2.11	   Start location: f3
3.51/2.11	
3.51/2.11	      8: f3 -> [3] : [ 0>=1+A ], cost: INF
3.51/2.11	
3.51/2.11	      9: f3 -> [3] : [ A>=1 ], cost: INF
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Computing asymptotic complexity for rule 8
3.51/2.11	
3.51/2.11	   Resulting cost INF has complexity: Nonterm
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Found new complexity Nonterm.
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	Obtained the following overall complexity (w.r.t. the length of the input n):
3.51/2.11	
3.51/2.11	   Complexity:  Nonterm
3.51/2.11	
3.51/2.11	   Cpx degree:  Nonterm
3.51/2.11	
3.51/2.11	   Solved cost: INF
3.51/2.11	
3.51/2.11	   Rule cost:   INF
3.51/2.11	
3.51/2.11	   Rule guard:  [ 0>=1+A ]
3.51/2.11	
3.51/2.11	
3.51/2.11	
3.51/2.11	NO
3.51/2.11	
3.51/2.11	
3.51/2.11	----------------------------------------
3.51/2.11	
3.51/2.11	(2)
3.51/2.11	BOUNDS(INF, INF)
3.88/2.13	EOF