3.52/1.83	WORST_CASE(NON_POLY, ?)
3.52/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.52/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.52/1.84	
3.52/1.84	
3.52/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.52/1.84	
3.52/1.84	(0) CpxIntTrs
3.52/1.84	(1) Loat Proof [FINISHED, 132 ms]
3.52/1.84	(2) BOUNDS(INF, INF)
3.52/1.84	
3.52/1.84	
3.52/1.84	----------------------------------------
3.52/1.84	
3.52/1.84	(0)
3.52/1.84	Obligation:
3.52/1.84	Complexity Int TRS consisting of the following rules:
3.52/1.84	f0(A, B) -> Com_1(f1(A, A)) :|: A >= B && A <= B
3.52/1.84	f1(A, B) -> Com_1(f1(A + 1, B + 1)) :|: TRUE
3.52/1.84	f1(A, B) -> Com_1(f2(A, B)) :|: TRUE
3.52/1.84	f1(A, B) -> Com_1(f10000(A, B)) :|: A >= B + 1
3.52/1.84	
3.52/1.84	The start-symbols are:[f0_2]
3.52/1.84	
3.52/1.84	
3.52/1.84	----------------------------------------
3.52/1.84	
3.52/1.84	(1) Loat Proof (FINISHED)
3.52/1.84	
3.52/1.84	
3.52/1.84	### Pre-processing the ITS problem ###
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Initial linear ITS problem
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      0: f0 -> f1 : B'=A, [ A==B ], cost: 1
3.52/1.84	
3.52/1.84	      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1
3.52/1.84	
3.52/1.84	      2: f1 -> f2 : [], cost: 1
3.52/1.84	
3.52/1.84	      3: f1 -> f10000 : [ A>=1+B ], cost: 1
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Removed unreachable and leaf rules:
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      0: f0 -> f1 : B'=A, [ A==B ], cost: 1
3.52/1.84	
3.52/1.84	      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	### Simplification by acceleration and chaining ###
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Accelerating simple loops of location 1.
3.52/1.84	
3.52/1.84	   Accelerating the following rules:
3.52/1.84	
3.52/1.84	      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	   Accelerated rule 1 with NONTERM, yielding the new rule 4.
3.52/1.84	
3.52/1.84	   Removing the simple loops: 1.
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Accelerated all simple loops using metering functions (where possible):
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      0: f0 -> f1 : B'=A, [ A==B ], cost: 1
3.52/1.84	
3.52/1.84	      4: f1 -> [4] : [], cost: INF
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Chained accelerated rules (with incoming rules):
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      0: f0 -> f1 : B'=A, [ A==B ], cost: 1
3.52/1.84	
3.52/1.84	      5: f0 -> [4] : B'=A, [ A==B ], cost: INF
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Removed unreachable locations (and leaf rules with constant cost):
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      5: f0 -> [4] : B'=A, [ A==B ], cost: INF
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	### Computing asymptotic complexity ###
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Fully simplified ITS problem
3.52/1.84	
3.52/1.84	   Start location: f0
3.52/1.84	
3.52/1.84	      5: f0 -> [4] : B'=A, [ A==B ], cost: INF
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Computing asymptotic complexity for rule 5
3.52/1.84	
3.52/1.84	   Resulting cost INF has complexity: Nonterm
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Found new complexity Nonterm.
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	Obtained the following overall complexity (w.r.t. the length of the input n):
3.52/1.84	
3.52/1.84	   Complexity:  Nonterm
3.52/1.84	
3.52/1.84	   Cpx degree:  Nonterm
3.52/1.84	
3.52/1.84	   Solved cost: INF
3.52/1.84	
3.52/1.84	   Rule cost:   INF
3.52/1.84	
3.52/1.84	   Rule guard:  [ A==B ]
3.52/1.84	
3.52/1.84	
3.52/1.84	
3.52/1.84	NO
3.52/1.84	
3.52/1.84	
3.52/1.84	----------------------------------------
3.52/1.84	
3.52/1.84	(2)
3.52/1.84	BOUNDS(INF, INF)
3.52/1.86	EOF