3.22/1.71	WORST_CASE(NON_POLY, ?)
3.22/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.22/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.22/1.72	
3.22/1.72	
3.22/1.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.22/1.72	
3.22/1.72	(0) CpxIntTrs
3.22/1.72	(1) Loat Proof [FINISHED, 133 ms]
3.22/1.72	(2) BOUNDS(INF, INF)
3.22/1.72	
3.22/1.72	
3.22/1.72	----------------------------------------
3.22/1.72	
3.22/1.72	(0)
3.22/1.72	Obligation:
3.22/1.72	Complexity Int TRS consisting of the following rules:
3.22/1.72	f0(A, B, C, D) -> Com_1(f3(A, E, C, D)) :|: A >= 10
3.22/1.72	f0(A, B, C, D) -> Com_1(f0(-(1) + A, B, A, D)) :|: 9 >= A
3.22/1.72	f1(A, B, C, D) -> Com_1(f0(-(1), B, C, -(1))) :|: 9 >= A
3.22/1.72	f2(A, B, C, D) -> Com_1(f0(0, B, C, D)) :|: TRUE
3.22/1.72	
3.22/1.72	The start-symbols are:[f2_4]
3.22/1.72	
3.22/1.72	
3.22/1.72	----------------------------------------
3.22/1.72	
3.22/1.72	(1) Loat Proof (FINISHED)
3.22/1.72	
3.22/1.72	
3.22/1.72	### Pre-processing the ITS problem ###
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Initial linear ITS problem
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      0: f0 -> f3 : B'=free, [ A>=10 ], cost: 1
3.22/1.72	
3.22/1.72	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.22/1.72	
3.22/1.72	      2: f1 -> f0 : A'=-1, D'=-1, [ 9>=A ], cost: 1
3.22/1.72	
3.22/1.72	      3: f2 -> f0 : A'=0, [], cost: 1
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Removed unreachable and leaf rules:
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.22/1.72	
3.22/1.72	      3: f2 -> f0 : A'=0, [], cost: 1
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	### Simplification by acceleration and chaining ###
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Accelerating simple loops of location 0.
3.22/1.72	
3.22/1.72	   Accelerating the following rules:
3.22/1.72	
3.22/1.72	      1: f0 -> f0 : A'=-1+A, C'=A, [ 9>=A ], cost: 1
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	   Accelerated rule 1 with NONTERM, yielding the new rule 4.
3.22/1.72	
3.22/1.72	   Removing the simple loops: 1.
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Accelerated all simple loops using metering functions (where possible):
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      4: f0 -> [4] : [ 9>=A ], cost: INF
3.22/1.72	
3.22/1.72	      3: f2 -> f0 : A'=0, [], cost: 1
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Chained accelerated rules (with incoming rules):
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      3: f2 -> f0 : A'=0, [], cost: 1
3.22/1.72	
3.22/1.72	      5: f2 -> [4] : A'=0, [], cost: INF
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Removed unreachable locations (and leaf rules with constant cost):
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      5: f2 -> [4] : A'=0, [], cost: INF
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	### Computing asymptotic complexity ###
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Fully simplified ITS problem
3.22/1.72	
3.22/1.72	   Start location: f2
3.22/1.72	
3.22/1.72	      5: f2 -> [4] : A'=0, [], cost: INF
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Computing asymptotic complexity for rule 5
3.22/1.72	
3.22/1.72	   Resulting cost INF has complexity: Nonterm
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Found new complexity Nonterm.
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	Obtained the following overall complexity (w.r.t. the length of the input n):
3.22/1.72	
3.22/1.72	   Complexity:  Nonterm
3.22/1.72	
3.22/1.72	   Cpx degree:  Nonterm
3.22/1.72	
3.22/1.72	   Solved cost: INF
3.22/1.72	
3.22/1.72	   Rule cost:   INF
3.22/1.72	
3.22/1.72	   Rule guard:  []
3.22/1.72	
3.22/1.72	
3.22/1.72	
3.22/1.72	NO
3.22/1.72	
3.22/1.72	
3.22/1.72	----------------------------------------
3.22/1.72	
3.22/1.72	(2)
3.22/1.72	BOUNDS(INF, INF)
3.22/1.76	EOF