3.72/1.77	WORST_CASE(NON_POLY, ?)
3.72/1.78	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.72/1.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.72/1.78	
3.72/1.78	
3.72/1.78	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.72/1.78	
3.72/1.78	(0) CpxIntTrs
3.72/1.78	(1) Loat Proof [FINISHED, 106 ms]
3.72/1.78	(2) BOUNDS(INF, INF)
3.72/1.78	
3.72/1.78	
3.72/1.78	----------------------------------------
3.72/1.78	
3.72/1.78	(0)
3.72/1.78	Obligation:
3.72/1.78	Complexity Int TRS consisting of the following rules:
3.72/1.78	f0(A, B, C, D) -> Com_1(f3(A, E, C, D)) :|: A >= 10
3.72/1.78	f0(A, B, C, D) -> Com_1(f0(-(1) + A, B, A, D)) :|: 9 >= A
3.72/1.78	f1(A, B, C, D) -> Com_1(f0(-(1), B, C, -(1))) :|: 9 >= A
3.72/1.78	f2(A, B, C, D) -> Com_1(f0(0, B, C, D)) :|: TRUE
3.72/1.78	
3.72/1.78	The start-symbols are:[f2_4]
3.72/1.78	
3.72/1.78	
3.72/1.78	----------------------------------------
3.72/1.78	
3.72/1.78	(1) Loat Proof (FINISHED)
3.72/1.78	
3.72/1.78	
3.72/1.78	### Pre-processing the ITS problem ###
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Initial linear ITS problem
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      0: f0 -> f3 : B'=free, [ A>=10 ], cost: 1
3.72/1.78	
3.72/1.78	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.72/1.78	
3.72/1.78	      2: f1 -> f0 : A'=-1, D'=-1, [ 9>=A ], cost: 1
3.72/1.78	
3.72/1.78	      3: f2 -> f0 : A'=0, [], cost: 1
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Removed unreachable and leaf rules:
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.72/1.78	
3.72/1.78	      3: f2 -> f0 : A'=0, [], cost: 1
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	### Simplification by acceleration and chaining ###
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Accelerating simple loops of location 0.
3.72/1.78	
3.72/1.78	   Accelerating the following rules:
3.72/1.78	
3.72/1.78	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	   Accelerated rule 1 with NONTERM, yielding the new rule 4.
3.72/1.78	
3.72/1.78	   Removing the simple loops: 1.
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Accelerated all simple loops using metering functions (where possible):
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      4: f0 -> [4] : [ 9>=A ], cost: INF
3.72/1.78	
3.72/1.78	      3: f2 -> f0 : A'=0, [], cost: 1
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Chained accelerated rules (with incoming rules):
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      3: f2 -> f0 : A'=0, [], cost: 1
3.72/1.78	
3.72/1.78	      5: f2 -> [4] : A'=0, [], cost: INF
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Removed unreachable locations (and leaf rules with constant cost):
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      5: f2 -> [4] : A'=0, [], cost: INF
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	### Computing asymptotic complexity ###
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Fully simplified ITS problem
3.72/1.78	
3.72/1.78	   Start location: f2
3.72/1.78	
3.72/1.78	      5: f2 -> [4] : A'=0, [], cost: INF
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Computing asymptotic complexity for rule 5
3.72/1.78	
3.72/1.78	   Resulting cost INF has complexity: Nonterm
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Found new complexity Nonterm.
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	Obtained the following overall complexity (w.r.t. the length of the input n):
3.72/1.78	
3.72/1.78	   Complexity:  Nonterm
3.72/1.78	
3.72/1.78	   Cpx degree:  Nonterm
3.72/1.78	
3.72/1.78	   Solved cost: INF
3.72/1.78	
3.72/1.78	   Rule cost:   INF
3.72/1.78	
3.72/1.78	   Rule guard:  []
3.72/1.78	
3.72/1.78	
3.72/1.78	
3.72/1.78	NO
3.72/1.78	
3.72/1.78	
3.72/1.78	----------------------------------------
3.72/1.78	
3.72/1.78	(2)
3.72/1.78	BOUNDS(INF, INF)
4.00/1.80	EOF