3.97/1.79	WORST_CASE(NON_POLY, ?)
4.08/1.79	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.08/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.08/1.79	
4.08/1.79	
4.08/1.79	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.08/1.79	
4.08/1.79	(0) CpxIntTrs
4.08/1.79	(1) Loat Proof [FINISHED, 69 ms]
4.08/1.79	(2) BOUNDS(INF, INF)
4.08/1.79	
4.08/1.79	
4.08/1.79	----------------------------------------
4.08/1.79	
4.08/1.79	(0)
4.08/1.79	Obligation:
4.08/1.79	Complexity Int TRS consisting of the following rules:
4.08/1.79	f3(A, B, C, D) -> Com_1(f1(0, B, C, D)) :|: TRUE
4.08/1.79	f1(A, B, C, D) -> Com_1(f2(A, B, C, E)) :|: B >= C
4.08/1.79	f1(A, B, C, D) -> Com_1(f2(1, 1 + B, C, E)) :|: B + 1 >= C && B + 1 <= C && A >= 0 && A <= 0
4.08/1.79	f1(A, B, C, D) -> Com_1(f1(0, 1 + B, 1 + C, D)) :|: C >= 2 + B && C >= 1 + B && A >= 0 && A <= 0
4.08/1.79	
4.08/1.79	The start-symbols are:[f3_4]
4.08/1.79	
4.08/1.79	
4.08/1.79	----------------------------------------
4.08/1.79	
4.08/1.79	(1) Loat Proof (FINISHED)
4.08/1.79	
4.08/1.79	
4.08/1.79	### Pre-processing the ITS problem ###
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Initial linear ITS problem
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      0: f3 -> f1 : A'=0, [], cost: 1
4.08/1.79	
4.08/1.79	      1: f1 -> f2 : D'=free, [ B>=C ], cost: 1
4.08/1.79	
4.08/1.79	      2: f1 -> f2 : A'=1, B'=1+B, D'=free_1, [ 1+B==C && A==0 ], cost: 1
4.08/1.79	
4.08/1.79	      3: f1 -> f1 : A'=0, B'=1+B, C'=1+C, [ C>=2+B && C>=1+B && A==0 ], cost: 1
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Removed unreachable and leaf rules:
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      0: f3 -> f1 : A'=0, [], cost: 1
4.08/1.79	
4.08/1.79	      3: f1 -> f1 : A'=0, B'=1+B, C'=1+C, [ C>=2+B && C>=1+B && A==0 ], cost: 1
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Simplified all rules, resulting in:
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      0: f3 -> f1 : A'=0, [], cost: 1
4.08/1.79	
4.08/1.79	      3: f1 -> f1 : A'=0, B'=1+B, C'=1+C, [ C>=2+B && A==0 ], cost: 1
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	### Simplification by acceleration and chaining ###
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Accelerating simple loops of location 1.
4.08/1.79	
4.08/1.79	   Accelerating the following rules:
4.08/1.79	
4.08/1.79	      3: f1 -> f1 : A'=0, B'=1+B, C'=1+C, [ C>=2+B && A==0 ], cost: 1
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	   Accelerated rule 3 with NONTERM, yielding the new rule 4.
4.08/1.79	
4.08/1.79	   Removing the simple loops: 3.
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Accelerated all simple loops using metering functions (where possible):
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      0: f3 -> f1 : A'=0, [], cost: 1
4.08/1.79	
4.08/1.79	      4: f1 -> [3] : [ C>=2+B && A==0 ], cost: INF
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Chained accelerated rules (with incoming rules):
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      0: f3 -> f1 : A'=0, [], cost: 1
4.08/1.79	
4.08/1.79	      5: f3 -> [3] : A'=0, [ C>=2+B ], cost: INF
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Removed unreachable locations (and leaf rules with constant cost):
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      5: f3 -> [3] : A'=0, [ C>=2+B ], cost: INF
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	### Computing asymptotic complexity ###
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Fully simplified ITS problem
4.08/1.79	
4.08/1.79	   Start location: f3
4.08/1.79	
4.08/1.79	      5: f3 -> [3] : A'=0, [ C>=2+B ], cost: INF
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Computing asymptotic complexity for rule 5
4.08/1.79	
4.08/1.79	   Resulting cost INF has complexity: Nonterm
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Found new complexity Nonterm.
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	Obtained the following overall complexity (w.r.t. the length of the input n):
4.08/1.79	
4.08/1.79	   Complexity:  Nonterm
4.08/1.79	
4.08/1.79	   Cpx degree:  Nonterm
4.08/1.79	
4.08/1.79	   Solved cost: INF
4.08/1.79	
4.08/1.79	   Rule cost:   INF
4.08/1.79	
4.08/1.79	   Rule guard:  [ C>=2+B ]
4.08/1.79	
4.08/1.79	
4.08/1.79	
4.08/1.79	NO
4.08/1.79	
4.08/1.79	
4.08/1.79	----------------------------------------
4.08/1.79	
4.08/1.79	(2)
4.08/1.79	BOUNDS(INF, INF)
4.08/1.82	EOF