4.18/1.94	WORST_CASE(NON_POLY, ?)
4.18/1.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.18/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.18/1.94	
4.18/1.94	
4.18/1.94	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.18/1.94	
4.18/1.94	(0) CpxIntTrs
4.18/1.94	(1) Loat Proof [FINISHED, 206 ms]
4.18/1.94	(2) BOUNDS(INF, INF)
4.18/1.94	
4.18/1.94	
4.18/1.94	----------------------------------------
4.18/1.94	
4.18/1.94	(0)
4.18/1.94	Obligation:
4.18/1.94	Complexity Int TRS consisting of the following rules:
4.18/1.94	f0(A, B, C) -> Com_1(f1(0, B, C)) :|: TRUE
4.18/1.94	f1(A, B, C) -> Com_1(f1(A, B - 1, D)) :|: B >= 1
4.18/1.94	f1(A, B, C) -> Com_1(f4(A, B, D)) :|: 0 >= B
4.18/1.94	f4(A, B, C) -> Com_1(f4(1, B, D)) :|: TRUE
4.18/1.94	
4.18/1.94	The start-symbols are:[f0_3]
4.18/1.94	
4.18/1.94	
4.18/1.94	----------------------------------------
4.18/1.94	
4.18/1.94	(1) Loat Proof (FINISHED)
4.18/1.94	
4.18/1.94	
4.18/1.94	### Pre-processing the ITS problem ###
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	Initial linear ITS problem
4.18/1.94	
4.18/1.94	   Start location: f0
4.18/1.94	
4.18/1.94	      0: f0 -> f1 : A'=0, [], cost: 1
4.18/1.94	
4.18/1.94	      1: f1 -> f1 : B'=-1+B, C'=free, [ B>=1 ], cost: 1
4.18/1.94	
4.18/1.94	      2: f1 -> f4 : C'=free_1, [ 0>=B ], cost: 1
4.18/1.94	
4.18/1.94	      3: f4 -> f4 : A'=1, C'=free_2, [], cost: 1
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	### Simplification by acceleration and chaining ###
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	Accelerating simple loops of location 1.
4.18/1.94	
4.18/1.94	   Accelerating the following rules:
4.18/1.94	
4.18/1.94	      1: f1 -> f1 : B'=-1+B, C'=free, [ B>=1 ], cost: 1
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	   Accelerated rule 1 with metering function B, yielding the new rule 4.
4.18/1.94	
4.18/1.94	   Removing the simple loops: 1.
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	Accelerating simple loops of location 2.
4.18/1.94	
4.18/1.94	   Accelerating the following rules:
4.18/1.94	
4.18/1.94	      3: f4 -> f4 : A'=1, C'=free_2, [], cost: 1
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	   Accelerated rule 3 with NONTERM, yielding the new rule 5.
4.18/1.94	
4.18/1.94	   Removing the simple loops: 3.
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	Accelerated all simple loops using metering functions (where possible):
4.18/1.94	
4.18/1.94	   Start location: f0
4.18/1.94	
4.18/1.94	      0: f0 -> f1 : A'=0, [], cost: 1
4.18/1.94	
4.18/1.94	      2: f1 -> f4 : C'=free_1, [ 0>=B ], cost: 1
4.18/1.94	
4.18/1.94	      4: f1 -> f1 : B'=0, C'=free, [ B>=1 ], cost: B
4.18/1.94	
4.18/1.94	      5: f4 -> [4] : [], cost: INF
4.18/1.94	
4.18/1.94	
4.18/1.94	
4.18/1.94	Chained accelerated rules (with incoming rules):
4.18/1.94	
4.18/1.94	   Start location: f0
4.18/1.94	
4.18/1.94	      0: f0 -> f1 : A'=0, [], cost: 1
4.18/1.94	
4.18/1.94	      6: f0 -> f1 : A'=0, B'=0, C'=free, [ B>=1 ], cost: 1+B
4.18/1.94	
4.18/1.94	      2: f1 -> f4 : C'=free_1, [ 0>=B ], cost: 1
4.18/1.94	
4.18/1.94	      7: f1 -> [4] : C'=free_1, [ 0>=B ], cost: INF
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Removed unreachable locations (and leaf rules with constant cost):
4.18/1.95	
4.18/1.95	   Start location: f0
4.18/1.95	
4.18/1.95	      0: f0 -> f1 : A'=0, [], cost: 1
4.18/1.95	
4.18/1.95	      6: f0 -> f1 : A'=0, B'=0, C'=free, [ B>=1 ], cost: 1+B
4.18/1.95	
4.18/1.95	      7: f1 -> [4] : C'=free_1, [ 0>=B ], cost: INF
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Eliminated locations (on tree-shaped paths):
4.18/1.95	
4.18/1.95	   Start location: f0
4.18/1.95	
4.18/1.95	      8: f0 -> [4] : A'=0, C'=free_1, [ 0>=B ], cost: INF
4.18/1.95	
4.18/1.95	      9: f0 -> [4] : A'=0, B'=0, C'=free_1, [ B>=1 ], cost: INF
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	### Computing asymptotic complexity ###
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Fully simplified ITS problem
4.18/1.95	
4.18/1.95	   Start location: f0
4.18/1.95	
4.18/1.95	      8: f0 -> [4] : A'=0, C'=free_1, [ 0>=B ], cost: INF
4.18/1.95	
4.18/1.95	      9: f0 -> [4] : A'=0, B'=0, C'=free_1, [ B>=1 ], cost: INF
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Computing asymptotic complexity for rule 8
4.18/1.95	
4.18/1.95	   Resulting cost INF has complexity: Nonterm
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Found new complexity Nonterm.
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	Obtained the following overall complexity (w.r.t. the length of the input n):
4.18/1.95	
4.18/1.95	   Complexity:  Nonterm
4.18/1.95	
4.18/1.95	   Cpx degree:  Nonterm
4.18/1.95	
4.18/1.95	   Solved cost: INF
4.18/1.95	
4.18/1.95	   Rule cost:   INF
4.18/1.95	
4.18/1.95	   Rule guard:  [ 0>=B ]
4.18/1.95	
4.18/1.95	
4.18/1.95	
4.18/1.95	NO
4.18/1.95	
4.18/1.95	
4.18/1.95	----------------------------------------
4.18/1.95	
4.18/1.95	(2)
4.18/1.95	BOUNDS(INF, INF)
4.18/1.97	EOF