6.00/3.09	MAYBE
6.08/3.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.08/3.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.08/3.10	
6.08/3.10	
6.08/3.10	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.08/3.10	
6.08/3.10	(0) CpxIntTrs
6.08/3.10	(1) Loat Proof [FINISHED, 627 ms]
6.08/3.10	(2) BOUNDS(1, INF)
6.08/3.10	
6.08/3.10	
6.08/3.10	----------------------------------------
6.08/3.10	
6.08/3.10	(0)
6.08/3.10	Obligation:
6.08/3.10	Complexity Int TRS consisting of the following rules:
6.08/3.10	f0(A, B, C, D, E, F) -> Com_1(f0(-(A), B + A, C + A, D, E, F)) :|: 0 >= A + 1
6.08/3.10	f0(A, B, C, D, E, F) -> Com_1(f0(A + B, -(B), C, D + B, E, F)) :|: 0 >= B + 1
6.08/3.10	f0(A, B, C, D, E, F) -> Com_1(f0(A, B + D, C, -(D), E + D, F)) :|: 0 >= D + 1
6.08/3.10	f0(A, B, C, D, E, F) -> Com_1(f0(A, B, C + E, D + E, -(E), F)) :|: 0 >= E + 1
6.08/3.10	f0(A, B, C, D, E, F) -> Com_1(f0(A + C, B, -(C), D, E + C, F)) :|: 0 >= C + 1
6.08/3.10	f1(A, B, C, D, E, F) -> Com_1(f0(G, H, K, I, J, G + H + I + J + K)) :|: G + H + I + J + K >= 1
6.08/3.10	
6.08/3.10	The start-symbols are:[f1_6]
6.08/3.10	
6.08/3.10	
6.08/3.10	----------------------------------------
6.08/3.10	
6.08/3.10	(1) Loat Proof (FINISHED)
6.08/3.10	
6.08/3.10	
6.08/3.10	### Pre-processing the ITS problem ###
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Initial linear ITS problem
6.08/3.10	
6.08/3.10	   Start location: f1
6.08/3.10	
6.08/3.10	      0: f0 -> f0 : A'=-A, B'=A+B, C'=C+A, [ 0>=1+A ], cost: 1
6.08/3.10	
6.08/3.10	      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1
6.08/3.10	
6.08/3.10	      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1
6.08/3.10	
6.08/3.10	      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1
6.08/3.10	
6.08/3.10	      4: f0 -> f0 : A'=C+A, C'=-C, E'=C+E, [ 0>=1+C ], cost: 1
6.08/3.10	
6.08/3.10	      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	### Simplification by acceleration and chaining ###
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Accelerating simple loops of location 0.
6.08/3.10	
6.08/3.10	   Accelerating the following rules:
6.08/3.10	
6.08/3.10	      0: f0 -> f0 : A'=-A, B'=A+B, C'=C+A, [ 0>=1+A ], cost: 1
6.08/3.10	
6.08/3.10	      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1
6.08/3.10	
6.08/3.10	      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1
6.08/3.10	
6.08/3.10	      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1
6.08/3.10	
6.08/3.10	      4: f0 -> f0 : A'=C+A, C'=-C, E'=C+E, [ 0>=1+C ], cost: 1
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	   Found no metering function for rule 0.
6.08/3.10	
6.08/3.10	   Found no metering function for rule 1.
6.08/3.10	
6.08/3.10	   Found no metering function for rule 2.
6.08/3.10	
6.08/3.10	   Found no metering function for rule 3.
6.08/3.10	
6.08/3.10	   Found no metering function for rule 4.
6.08/3.10	
6.08/3.10	   Removing the simple loops:.
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Accelerated all simple loops using metering functions (where possible):
6.08/3.10	
6.08/3.10	   Start location: f1
6.08/3.10	
6.08/3.10	      0: f0 -> f0 : A'=-A, B'=A+B, C'=C+A, [ 0>=1+A ], cost: 1
6.08/3.10	
6.08/3.10	      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1
6.08/3.10	
6.08/3.10	      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1
6.08/3.10	
6.08/3.10	      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1
6.08/3.10	
6.08/3.10	      4: f0 -> f0 : A'=C+A, C'=-C, E'=C+E, [ 0>=1+C ], cost: 1
6.08/3.10	
6.08/3.10	      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Chained accelerated rules (with incoming rules):
6.08/3.10	
6.08/3.10	   Start location: f1
6.08/3.10	
6.08/3.10	      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1
6.08/3.10	
6.08/3.10	      6: f1 -> f0 : A'=-free_2, B'=free_4+free_2, C'=free_2+free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_2 ], cost: 2
6.08/3.10	
6.08/3.10	      7: f1 -> f0 : A'=free_4+free_2, B'=-free_4, C'=free_3, D'=free+free_4, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_4 ], cost: 2
6.08/3.10	
6.08/3.10	      8: f1 -> f0 : A'=free_2, B'=free+free_4, C'=free_3, D'=-free, E'=free+free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free ], cost: 2
6.08/3.10	
6.08/3.10	      9: f1 -> f0 : A'=free_2, B'=free_4, C'=free_1+free_3, D'=free+free_1, E'=-free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_1 ], cost: 2
6.08/3.10	
6.08/3.10	     10: f1 -> f0 : A'=free_2+free_3, B'=free_4, C'=-free_3, D'=free, E'=free_1+free_3, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_3 ], cost: 2
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Removed unreachable locations (and leaf rules with constant cost):
6.08/3.10	
6.08/3.10	   Start location: f1
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	### Computing asymptotic complexity ###
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Fully simplified ITS problem
6.08/3.10	
6.08/3.10	   Start location: f1
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	Obtained the following overall complexity (w.r.t. the length of the input n):
6.08/3.10	
6.08/3.10	   Complexity:  Unknown
6.08/3.10	
6.08/3.10	   Cpx degree:  ?
6.08/3.10	
6.08/3.10	   Solved cost: 0
6.08/3.10	
6.08/3.10	   Rule cost:   0
6.08/3.10	
6.08/3.10	   Rule guard:  []
6.08/3.10	
6.08/3.10	
6.08/3.10	
6.08/3.10	WORST_CASE(Omega(0),?)
6.08/3.10	
6.08/3.10	
6.08/3.10	----------------------------------------
6.08/3.10	
6.08/3.10	(2)
6.08/3.10	BOUNDS(1, INF)
6.08/3.12	EOF