5.11/2.86	MAYBE
5.11/2.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.11/2.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.11/2.86	
5.11/2.86	
5.11/2.86	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.11/2.86	
5.11/2.86	(0) CpxIntTrs
5.11/2.86	(1) Loat Proof [FINISHED, 117 ms]
5.11/2.86	(2) BOUNDS(1, INF)
5.11/2.86	
5.11/2.86	
5.11/2.86	----------------------------------------
5.11/2.86	
5.11/2.86	(0)
5.11/2.86	Obligation:
5.11/2.86	Complexity Int TRS consisting of the following rules:
5.11/2.86	f4(A, B, C, D, E, F, G) -> Com_1(f4(A - B, B, C, D, E, F, G)) :|: A >= 0
5.11/2.86	f4(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: 0 >= A + 1
5.11/2.86	f5(A, B, C, D, E, F, G) -> Com_1(f4(A, B, C, D, E, F, G)) :|: 0 >= B + 1
5.11/2.86	f5(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: B >= 0
5.11/2.86	
5.11/2.86	The start-symbols are:[f5_7]
5.11/2.86	
5.11/2.86	
5.11/2.86	----------------------------------------
5.11/2.86	
5.11/2.86	(1) Loat Proof (FINISHED)
5.11/2.86	
5.11/2.86	
5.11/2.86	### Pre-processing the ITS problem ###
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Initial linear ITS problem
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1
5.11/2.86	
5.11/2.86	      1: f4 -> f6 : C'=0, D'=0, E'=0, F'=0, G'=0, [ 0>=1+A ], cost: 1
5.11/2.86	
5.11/2.86	      2: f5 -> f4 : [ 0>=1+B ], cost: 1
5.11/2.86	
5.11/2.86	      3: f5 -> f6 : C'=0, D'=0, E'=0, F'=0, G'=0, [ B>=0 ], cost: 1
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Removed unreachable and leaf rules:
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1
5.11/2.86	
5.11/2.86	      2: f5 -> f4 : [ 0>=1+B ], cost: 1
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	### Simplification by acceleration and chaining ###
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Accelerating simple loops of location 0.
5.11/2.86	
5.11/2.86	   Accelerating the following rules:
5.11/2.86	
5.11/2.86	      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	   Found no metering function for rule 0.
5.11/2.86	
5.11/2.86	   Removing the simple loops:.
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Accelerated all simple loops using metering functions (where possible):
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1
5.11/2.86	
5.11/2.86	      2: f5 -> f4 : [ 0>=1+B ], cost: 1
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Chained accelerated rules (with incoming rules):
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	      2: f5 -> f4 : [ 0>=1+B ], cost: 1
5.11/2.86	
5.11/2.86	      4: f5 -> f4 : A'=A-B, [ 0>=1+B && A>=0 ], cost: 2
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Removed unreachable locations (and leaf rules with constant cost):
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	### Computing asymptotic complexity ###
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Fully simplified ITS problem
5.11/2.86	
5.11/2.86	   Start location: f5
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	Obtained the following overall complexity (w.r.t. the length of the input n):
5.11/2.86	
5.11/2.86	   Complexity:  Unknown
5.11/2.86	
5.11/2.86	   Cpx degree:  ?
5.11/2.86	
5.11/2.86	   Solved cost: 0
5.11/2.86	
5.11/2.86	   Rule cost:   0
5.11/2.86	
5.11/2.86	   Rule guard:  []
5.11/2.86	
5.11/2.86	
5.11/2.86	
5.11/2.86	WORST_CASE(Omega(0),?)
5.11/2.86	
5.11/2.86	
5.11/2.86	----------------------------------------
5.11/2.86	
5.11/2.86	(2)
5.11/2.86	BOUNDS(1, INF)
5.20/2.90	EOF