3.68/2.13	WORST_CASE(NON_POLY, ?)
3.68/2.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.68/2.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.68/2.14	
3.68/2.14	
3.68/2.14	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.68/2.14	
3.68/2.14	(0) CpxIntTrs
3.68/2.14	(1) Loat Proof [FINISHED, 195 ms]
3.68/2.14	(2) BOUNDS(INF, INF)
3.68/2.14	
3.68/2.14	
3.68/2.14	----------------------------------------
3.68/2.14	
3.68/2.14	(0)
3.68/2.14	Obligation:
3.68/2.14	Complexity Int TRS consisting of the following rules:
3.68/2.14	f3(A, B) -> Com_1(f0(0, B)) :|: TRUE
3.68/2.14	f0(A, B) -> Com_1(f0(A, B - 1)) :|: B >= 1
3.68/2.14	f4(A, B) -> Com_1(f4(A, B)) :|: TRUE
3.68/2.14	f0(A, B) -> Com_1(f4(-(1), B)) :|: 0 >= B
3.68/2.14	
3.68/2.14	The start-symbols are:[f3_2]
3.68/2.14	
3.68/2.14	
3.68/2.14	----------------------------------------
3.68/2.14	
3.68/2.14	(1) Loat Proof (FINISHED)
3.68/2.14	
3.68/2.14	
3.68/2.14	### Pre-processing the ITS problem ###
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Initial linear ITS problem
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      0: f3 -> f0 : A'=0, [], cost: 1
3.68/2.14	
3.68/2.14	      1: f0 -> f0 : B'=-1+B, [ B>=1 ], cost: 1
3.68/2.14	
3.68/2.14	      3: f0 -> f4 : A'=-1, [ 0>=B ], cost: 1
3.68/2.14	
3.68/2.14	      2: f4 -> f4 : [], cost: 1
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	### Simplification by acceleration and chaining ###
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Accelerating simple loops of location 1.
3.68/2.14	
3.68/2.14	   Accelerating the following rules:
3.68/2.14	
3.68/2.14	      1: f0 -> f0 : B'=-1+B, [ B>=1 ], cost: 1
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	   Accelerated rule 1 with metering function B, yielding the new rule 4.
3.68/2.14	
3.68/2.14	   Removing the simple loops: 1.
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Accelerating simple loops of location 2.
3.68/2.14	
3.68/2.14	   Accelerating the following rules:
3.68/2.14	
3.68/2.14	      2: f4 -> f4 : [], cost: 1
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	   Accelerated rule 2 with NONTERM, yielding the new rule 5.
3.68/2.14	
3.68/2.14	   Removing the simple loops: 2.
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Accelerated all simple loops using metering functions (where possible):
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      0: f3 -> f0 : A'=0, [], cost: 1
3.68/2.14	
3.68/2.14	      3: f0 -> f4 : A'=-1, [ 0>=B ], cost: 1
3.68/2.14	
3.68/2.14	      4: f0 -> f0 : B'=0, [ B>=1 ], cost: B
3.68/2.14	
3.68/2.14	      5: f4 -> [4] : [], cost: INF
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Chained accelerated rules (with incoming rules):
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      0: f3 -> f0 : A'=0, [], cost: 1
3.68/2.14	
3.68/2.14	      6: f3 -> f0 : A'=0, B'=0, [ B>=1 ], cost: 1+B
3.68/2.14	
3.68/2.14	      3: f0 -> f4 : A'=-1, [ 0>=B ], cost: 1
3.68/2.14	
3.68/2.14	      7: f0 -> [4] : A'=-1, [ 0>=B ], cost: INF
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Removed unreachable locations (and leaf rules with constant cost):
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      0: f3 -> f0 : A'=0, [], cost: 1
3.68/2.14	
3.68/2.14	      6: f3 -> f0 : A'=0, B'=0, [ B>=1 ], cost: 1+B
3.68/2.14	
3.68/2.14	      7: f0 -> [4] : A'=-1, [ 0>=B ], cost: INF
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Eliminated locations (on tree-shaped paths):
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      8: f3 -> [4] : A'=-1, [ 0>=B ], cost: INF
3.68/2.14	
3.68/2.14	      9: f3 -> [4] : A'=-1, B'=0, [ B>=1 ], cost: INF
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	### Computing asymptotic complexity ###
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Fully simplified ITS problem
3.68/2.14	
3.68/2.14	   Start location: f3
3.68/2.14	
3.68/2.14	      8: f3 -> [4] : A'=-1, [ 0>=B ], cost: INF
3.68/2.14	
3.68/2.14	      9: f3 -> [4] : A'=-1, B'=0, [ B>=1 ], cost: INF
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Computing asymptotic complexity for rule 8
3.68/2.14	
3.68/2.14	   Resulting cost INF has complexity: Nonterm
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Found new complexity Nonterm.
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	Obtained the following overall complexity (w.r.t. the length of the input n):
3.68/2.14	
3.68/2.14	   Complexity:  Nonterm
3.68/2.14	
3.68/2.14	   Cpx degree:  Nonterm
3.68/2.14	
3.68/2.14	   Solved cost: INF
3.68/2.14	
3.68/2.14	   Rule cost:   INF
3.68/2.14	
3.68/2.14	   Rule guard:  [ 0>=B ]
3.68/2.14	
3.68/2.14	
3.68/2.14	
3.68/2.14	NO
3.68/2.14	
3.68/2.14	
3.68/2.14	----------------------------------------
3.68/2.14	
3.68/2.14	(2)
3.68/2.14	BOUNDS(INF, INF)
3.68/2.15	EOF