4.35/1.94	WORST_CASE(NON_POLY, ?)
4.46/1.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.46/1.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.46/1.95	
4.46/1.95	
4.46/1.95	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.46/1.95	
4.46/1.95	(0) CpxIntTrs
4.46/1.95	(1) Loat Proof [FINISHED, 299 ms]
4.46/1.95	(2) BOUNDS(INF, INF)
4.46/1.95	
4.46/1.95	
4.46/1.95	----------------------------------------
4.46/1.95	
4.46/1.95	(0)
4.46/1.95	Obligation:
4.46/1.95	Complexity Int TRS consisting of the following rules:
4.46/1.95	f2(A, B, C, D) -> Com_1(f300(A, B, C, D)) :|: TRUE
4.46/1.95	f300(A, B, C, D) -> Com_1(f300(A, B, E, D)) :|: E >= 1 && B >= 1 + A
4.46/1.95	f300(A, B, C, D) -> Com_1(f300(A, B, E, D)) :|: 0 >= E + 1 && B >= 1 + A
4.46/1.95	f300(A, B, C, D) -> Com_1(f300(A, -(1) + B, 0, D)) :|: B >= 1 + A
4.46/1.95	f300(A, B, C, D) -> Com_1(f1(A, B, C, E)) :|: A >= B
4.46/1.95	
4.46/1.95	The start-symbols are:[f2_4]
4.46/1.95	
4.46/1.95	
4.46/1.95	----------------------------------------
4.46/1.95	
4.46/1.95	(1) Loat Proof (FINISHED)
4.46/1.95	
4.46/1.95	
4.46/1.95	### Pre-processing the ITS problem ###
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Initial linear ITS problem
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      0: f2 -> f300 : [], cost: 1
4.46/1.95	
4.46/1.95	      1: f300 -> f300 : C'=free, [ free>=1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      2: f300 -> f300 : C'=free_1, [ 0>=1+free_1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      3: f300 -> f300 : A'=-1+A, C'=0, [ A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      4: f300 -> f1 : D'=free_2, [ B>=A ], cost: 1
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Removed unreachable and leaf rules:
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      0: f2 -> f300 : [], cost: 1
4.46/1.95	
4.46/1.95	      1: f300 -> f300 : C'=free, [ free>=1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      2: f300 -> f300 : C'=free_1, [ 0>=1+free_1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      3: f300 -> f300 : A'=-1+A, C'=0, [ A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	### Simplification by acceleration and chaining ###
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Accelerating simple loops of location 1.
4.46/1.95	
4.46/1.95	   Accelerating the following rules:
4.46/1.95	
4.46/1.95	      1: f300 -> f300 : C'=free, [ free>=1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      2: f300 -> f300 : C'=free_1, [ 0>=1+free_1 && A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	      3: f300 -> f300 : A'=-1+A, C'=0, [ A>=1+B ], cost: 1
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	   Accelerated rule 1 with NONTERM, yielding the new rule 5.
4.46/1.95	
4.46/1.95	   Accelerated rule 2 with NONTERM, yielding the new rule 6.
4.46/1.95	
4.46/1.95	   Accelerated rule 3 with metering function A-B, yielding the new rule 7.
4.46/1.95	
4.46/1.95	   Removing the simple loops: 1 2 3.
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Accelerated all simple loops using metering functions (where possible):
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      0: f2 -> f300 : [], cost: 1
4.46/1.95	
4.46/1.95	      5: f300 -> [3] : [ free>=1 && A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	      6: f300 -> [3] : [ 0>=1+free_1 && A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	      7: f300 -> f300 : A'=B, C'=0, [ A>=1+B ], cost: A-B
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Chained accelerated rules (with incoming rules):
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      0: f2 -> f300 : [], cost: 1
4.46/1.95	
4.46/1.95	      8: f2 -> [3] : [ A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	      9: f2 -> [3] : [ A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	     10: f2 -> f300 : A'=B, C'=0, [ A>=1+B ], cost: 1+A-B
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Removed unreachable locations (and leaf rules with constant cost):
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      8: f2 -> [3] : [ A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	      9: f2 -> [3] : [ A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	     10: f2 -> f300 : A'=B, C'=0, [ A>=1+B ], cost: 1+A-B
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	### Computing asymptotic complexity ###
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Fully simplified ITS problem
4.46/1.95	
4.46/1.95	   Start location: f2
4.46/1.95	
4.46/1.95	      9: f2 -> [3] : [ A>=1+B ], cost: INF
4.46/1.95	
4.46/1.95	     10: f2 -> f300 : A'=B, C'=0, [ A>=1+B ], cost: 1+A-B
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Computing asymptotic complexity for rule 9
4.46/1.95	
4.46/1.95	   Resulting cost INF has complexity: Nonterm
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Found new complexity Nonterm.
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	Obtained the following overall complexity (w.r.t. the length of the input n):
4.46/1.95	
4.46/1.95	   Complexity:  Nonterm
4.46/1.95	
4.46/1.95	   Cpx degree:  Nonterm
4.46/1.95	
4.46/1.95	   Solved cost: INF
4.46/1.95	
4.46/1.95	   Rule cost:   INF
4.46/1.95	
4.46/1.95	   Rule guard:  [ A>=1+B ]
4.46/1.95	
4.46/1.95	
4.46/1.95	
4.46/1.95	NO
4.46/1.95	
4.46/1.95	
4.46/1.95	----------------------------------------
4.46/1.95	
4.46/1.95	(2)
4.46/1.95	BOUNDS(INF, INF)
4.46/1.98	EOF