3.90/1.97	WORST_CASE(NON_POLY, ?)
3.98/1.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.98/1.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.98/1.98	
3.98/1.98	
3.98/1.98	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.98/1.98	
3.98/1.98	(0) CpxIntTrs
3.98/1.98	(1) Loat Proof [FINISHED, 323 ms]
3.98/1.98	(2) BOUNDS(INF, INF)
3.98/1.98	
3.98/1.98	
3.98/1.98	----------------------------------------
3.98/1.98	
3.98/1.98	(0)
3.98/1.98	Obligation:
3.98/1.98	Complexity Int TRS consisting of the following rules:
3.98/1.98	f0(A, B) -> Com_1(f4(0, 99)) :|: TRUE
3.98/1.98	f4(A, B) -> Com_1(f4(E, B)) :|: B >= A + 1 && C >= D + 1
3.98/1.98	f4(A, B) -> Com_1(f4(A, E)) :|: B >= A + 1
3.98/1.98	f4(A, B) -> Com_1(f11(A, B)) :|: A >= B
3.98/1.98	
3.98/1.98	The start-symbols are:[f0_2]
3.98/1.98	
3.98/1.98	
3.98/1.98	----------------------------------------
3.98/1.98	
3.98/1.98	(1) Loat Proof (FINISHED)
3.98/1.98	
3.98/1.98	
3.98/1.98	### Pre-processing the ITS problem ###
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Initial linear ITS problem
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      0: f0 -> f4 : A'=0, B'=99, [], cost: 1
3.98/1.98	
3.98/1.98	      1: f4 -> f4 : A'=free_2, [ B>=1+A && free>=1+free_1 ], cost: 1
3.98/1.98	
3.98/1.98	      2: f4 -> f4 : B'=free_3, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	      3: f4 -> f11 : [ A>=B ], cost: 1
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Removed unreachable and leaf rules:
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      0: f0 -> f4 : A'=0, B'=99, [], cost: 1
3.98/1.98	
3.98/1.98	      1: f4 -> f4 : A'=free_2, [ B>=1+A && free>=1+free_1 ], cost: 1
3.98/1.98	
3.98/1.98	      2: f4 -> f4 : B'=free_3, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Simplified all rules, resulting in:
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      0: f0 -> f4 : A'=0, B'=99, [], cost: 1
3.98/1.98	
3.98/1.98	      1: f4 -> f4 : A'=free_2, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	      2: f4 -> f4 : B'=free_3, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	### Simplification by acceleration and chaining ###
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Accelerating simple loops of location 1.
3.98/1.98	
3.98/1.98	   Accelerating the following rules:
3.98/1.98	
3.98/1.98	      1: f4 -> f4 : A'=free_2, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	      2: f4 -> f4 : B'=free_3, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	   Accelerated rule 1 with NONTERM (after strengthening guard), yielding the new rule 4.
3.98/1.98	
3.98/1.98	   Accelerated rule 2 with NONTERM (after strengthening guard), yielding the new rule 5.
3.98/1.98	
3.98/1.98	   Removing the simple loops:.
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Accelerated all simple loops using metering functions (where possible):
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      0: f0 -> f4 : A'=0, B'=99, [], cost: 1
3.98/1.98	
3.98/1.98	      1: f4 -> f4 : A'=free_2, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	      2: f4 -> f4 : B'=free_3, [ B>=1+A ], cost: 1
3.98/1.98	
3.98/1.98	      4: f4 -> [3] : [ B>=1+A && B>=1+free_2 ], cost: INF
3.98/1.98	
3.98/1.98	      5: f4 -> [3] : [ B>=1+A && free_3>=1+A ], cost: INF
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Chained accelerated rules (with incoming rules):
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      0: f0 -> f4 : A'=0, B'=99, [], cost: 1
3.98/1.98	
3.98/1.98	      6: f0 -> f4 : A'=free_2, B'=99, [], cost: 2
3.98/1.98	
3.98/1.98	      7: f0 -> f4 : A'=0, B'=free_3, [], cost: 2
3.98/1.98	
3.98/1.98	      8: f0 -> [3] : A'=0, B'=99, [], cost: INF
3.98/1.98	
3.98/1.98	      9: f0 -> [3] : A'=0, B'=99, [], cost: INF
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Removed unreachable locations (and leaf rules with constant cost):
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      8: f0 -> [3] : A'=0, B'=99, [], cost: INF
3.98/1.98	
3.98/1.98	      9: f0 -> [3] : A'=0, B'=99, [], cost: INF
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	### Computing asymptotic complexity ###
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Fully simplified ITS problem
3.98/1.98	
3.98/1.98	   Start location: f0
3.98/1.98	
3.98/1.98	      9: f0 -> [3] : A'=0, B'=99, [], cost: INF
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Computing asymptotic complexity for rule 9
3.98/1.98	
3.98/1.98	   Resulting cost INF has complexity: Nonterm
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Found new complexity Nonterm.
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	Obtained the following overall complexity (w.r.t. the length of the input n):
3.98/1.98	
3.98/1.98	   Complexity:  Nonterm
3.98/1.98	
3.98/1.98	   Cpx degree:  Nonterm
3.98/1.98	
3.98/1.98	   Solved cost: INF
3.98/1.98	
3.98/1.98	   Rule cost:   INF
3.98/1.98	
3.98/1.98	   Rule guard:  []
3.98/1.98	
3.98/1.98	
3.98/1.98	
3.98/1.98	NO
3.98/1.98	
3.98/1.98	
3.98/1.98	----------------------------------------
3.98/1.98	
3.98/1.98	(2)
3.98/1.98	BOUNDS(INF, INF)
3.98/2.01	EOF