4.32/2.02	WORST_CASE(NON_POLY, ?)
4.32/2.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.32/2.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.32/2.02	
4.32/2.02	
4.32/2.02	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.32/2.02	
4.32/2.02	(0) CpxIntTrs
4.32/2.02	(1) Loat Proof [FINISHED, 328 ms]
4.32/2.02	(2) BOUNDS(INF, INF)
4.32/2.02	
4.32/2.02	
4.32/2.02	----------------------------------------
4.32/2.02	
4.32/2.02	(0)
4.32/2.02	Obligation:
4.32/2.02	Complexity Int TRS consisting of the following rules:
4.32/2.02	f2(A, B, C) -> Com_1(f2(A + 1, B, C)) :|: TRUE
4.32/2.02	f3(A, B, C) -> Com_1(f3(A, B - 1, C)) :|: B >= 1
4.32/2.02	f5(A, B, C) -> Com_1(f5(A, B, 1)) :|: TRUE
4.32/2.02	f0(A, B, C) -> Com_1(f2(0, B, C)) :|: C >= 1
4.32/2.02	f0(A, B, C) -> Com_1(f3(0, B, C)) :|: 0 >= C
4.32/2.02	f3(A, B, C) -> Com_1(f5(0, B, C)) :|: 0 >= B
4.32/2.02	
4.32/2.02	The start-symbols are:[f0_3]
4.32/2.02	
4.32/2.02	
4.32/2.02	----------------------------------------
4.32/2.02	
4.32/2.02	(1) Loat Proof (FINISHED)
4.32/2.02	
4.32/2.02	
4.32/2.02	### Pre-processing the ITS problem ###
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Initial linear ITS problem
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	      0: f2 -> f2 : A'=1+A, [], cost: 1
4.32/2.02	
4.32/2.02	      1: f3 -> f3 : B'=-1+B, [ B>=1 ], cost: 1
4.32/2.02	
4.32/2.02	      5: f3 -> f5 : A'=0, [ 0>=B ], cost: 1
4.32/2.02	
4.32/2.02	      2: f5 -> f5 : C'=1, [], cost: 1
4.32/2.02	
4.32/2.02	      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1
4.32/2.02	
4.32/2.02	      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	### Simplification by acceleration and chaining ###
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Accelerating simple loops of location 0.
4.32/2.02	
4.32/2.02	   Accelerating the following rules:
4.32/2.02	
4.32/2.02	      0: f2 -> f2 : A'=1+A, [], cost: 1
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	   Accelerated rule 0 with NONTERM, yielding the new rule 6.
4.32/2.02	
4.32/2.02	   Removing the simple loops: 0.
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Accelerating simple loops of location 1.
4.32/2.02	
4.32/2.02	   Accelerating the following rules:
4.32/2.02	
4.32/2.02	      1: f3 -> f3 : B'=-1+B, [ B>=1 ], cost: 1
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	   Accelerated rule 1 with metering function B, yielding the new rule 7.
4.32/2.02	
4.32/2.02	   Removing the simple loops: 1.
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Accelerating simple loops of location 2.
4.32/2.02	
4.32/2.02	   Accelerating the following rules:
4.32/2.02	
4.32/2.02	      2: f5 -> f5 : C'=1, [], cost: 1
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.32/2.02	
4.32/2.02	   Removing the simple loops: 2.
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Accelerated all simple loops using metering functions (where possible):
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	      6: f2 -> [4] : [], cost: INF
4.32/2.02	
4.32/2.02	      5: f3 -> f5 : A'=0, [ 0>=B ], cost: 1
4.32/2.02	
4.32/2.02	      7: f3 -> f3 : B'=0, [ B>=1 ], cost: B
4.32/2.02	
4.32/2.02	      8: f5 -> [6] : [], cost: INF
4.32/2.02	
4.32/2.02	      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1
4.32/2.02	
4.32/2.02	      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Chained accelerated rules (with incoming rules):
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	      5: f3 -> f5 : A'=0, [ 0>=B ], cost: 1
4.32/2.02	
4.32/2.02	     11: f3 -> [6] : A'=0, [ 0>=B ], cost: INF
4.32/2.02	
4.32/2.02	      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1
4.32/2.02	
4.32/2.02	      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1
4.32/2.02	
4.32/2.02	      9: f0 -> [4] : A'=0, [ C>=1 ], cost: INF
4.32/2.02	
4.32/2.02	     10: f0 -> f3 : A'=0, B'=0, [ 0>=C && B>=1 ], cost: 1+B
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Removed unreachable locations (and leaf rules with constant cost):
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	     11: f3 -> [6] : A'=0, [ 0>=B ], cost: INF
4.32/2.02	
4.32/2.02	      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1
4.32/2.02	
4.32/2.02	      9: f0 -> [4] : A'=0, [ C>=1 ], cost: INF
4.32/2.02	
4.32/2.02	     10: f0 -> f3 : A'=0, B'=0, [ 0>=C && B>=1 ], cost: 1+B
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Eliminated locations (on tree-shaped paths):
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	      9: f0 -> [4] : A'=0, [ C>=1 ], cost: INF
4.32/2.02	
4.32/2.02	     12: f0 -> [6] : A'=0, [ 0>=C && 0>=B ], cost: INF
4.32/2.02	
4.32/2.02	     13: f0 -> [6] : A'=0, B'=0, [ 0>=C && B>=1 ], cost: INF
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	### Computing asymptotic complexity ###
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Fully simplified ITS problem
4.32/2.02	
4.32/2.02	   Start location: f0
4.32/2.02	
4.32/2.02	      9: f0 -> [4] : A'=0, [ C>=1 ], cost: INF
4.32/2.02	
4.32/2.02	     12: f0 -> [6] : A'=0, [ 0>=C && 0>=B ], cost: INF
4.32/2.02	
4.32/2.02	     13: f0 -> [6] : A'=0, B'=0, [ 0>=C && B>=1 ], cost: INF
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Computing asymptotic complexity for rule 9
4.32/2.02	
4.32/2.02	   Resulting cost INF has complexity: Nonterm
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Found new complexity Nonterm.
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	Obtained the following overall complexity (w.r.t. the length of the input n):
4.32/2.02	
4.32/2.02	   Complexity:  Nonterm
4.32/2.02	
4.32/2.02	   Cpx degree:  Nonterm
4.32/2.02	
4.32/2.02	   Solved cost: INF
4.32/2.02	
4.32/2.02	   Rule cost:   INF
4.32/2.02	
4.32/2.02	   Rule guard:  [ C>=1 ]
4.32/2.02	
4.32/2.02	
4.32/2.02	
4.32/2.02	NO
4.32/2.02	
4.32/2.02	
4.32/2.02	----------------------------------------
4.32/2.02	
4.32/2.02	(2)
4.32/2.02	BOUNDS(INF, INF)
4.32/2.04	EOF