4.89/2.41	WORST_CASE(NON_POLY, ?)
4.89/2.41	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.89/2.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.89/2.41	
4.89/2.41	
4.89/2.41	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.89/2.41	
4.89/2.41	(0) CpxIntTrs
4.89/2.41	(1) Loat Proof [FINISHED, 691 ms]
4.89/2.41	(2) BOUNDS(INF, INF)
4.89/2.41	
4.89/2.41	
4.89/2.41	----------------------------------------
4.89/2.41	
4.89/2.41	(0)
4.89/2.41	Obligation:
4.89/2.41	Complexity Int TRS consisting of the following rules:
4.89/2.41	f11(A, B, C, D, E, F) -> Com_1(f11(A - 2, B - 1, C + 1, G, E, F)) :|: A >= 1 && G >= 1
4.89/2.41	f11(A, B, C, D, E, F) -> Com_1(f11(A - 2, B, C, G, E, F)) :|: 0 >= G && A >= 1 && A >= B + 1
4.89/2.41	f21(A, B, C, D, E, F) -> Com_1(f21(A, B, C, D, E, F)) :|: TRUE
4.89/2.41	f23(A, B, C, D, E, F) -> Com_1(f26(A, B, C, D, E, F)) :|: TRUE
4.89/2.41	f11(A, B, C, D, E, F) -> Com_1(f21(A, B, C, D, E, F)) :|: 0 >= A
4.89/2.41	f0(A, B, C, D, E, F) -> Com_1(f11(4, G, 0, D, G, 4)) :|: G >= 1
4.89/2.41	
4.89/2.41	The start-symbols are:[f0_6]
4.89/2.41	
4.89/2.41	
4.89/2.41	----------------------------------------
4.89/2.41	
4.89/2.41	(1) Loat Proof (FINISHED)
4.89/2.41	
4.89/2.41	
4.89/2.41	### Pre-processing the ITS problem ###
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Initial linear ITS problem
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	      0: f11 -> f11 : A'=-2+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.89/2.41	
4.89/2.41	      1: f11 -> f11 : A'=-2+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.89/2.41	
4.89/2.41	      4: f11 -> f21 : [ 0>=A ], cost: 1
4.89/2.41	
4.89/2.41	      2: f21 -> f21 : [], cost: 1
4.89/2.41	
4.89/2.41	      3: f23 -> f26 : [], cost: 1
4.89/2.41	
4.89/2.41	      5: f0 -> f11 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Removed unreachable and leaf rules:
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	      0: f11 -> f11 : A'=-2+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.89/2.41	
4.89/2.41	      1: f11 -> f11 : A'=-2+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.89/2.41	
4.89/2.41	      4: f11 -> f21 : [ 0>=A ], cost: 1
4.89/2.41	
4.89/2.41	      2: f21 -> f21 : [], cost: 1
4.89/2.41	
4.89/2.41	      5: f0 -> f11 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	### Simplification by acceleration and chaining ###
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Accelerating simple loops of location 0.
4.89/2.41	
4.89/2.41	   Accelerating the following rules:
4.89/2.41	
4.89/2.41	      0: f11 -> f11 : A'=-2+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.89/2.41	
4.89/2.41	      1: f11 -> f11 : A'=-2+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	   Accelerated rule 0 with metering function meter (where 2*meter==A), yielding the new rule 6.
4.89/2.41	
4.89/2.41	   Accelerated rule 1 with backward acceleration, yielding the new rule 7.
4.89/2.41	
4.89/2.41	      During metering: Instantiating temporary variables by {meter==1}
4.89/2.41	
4.89/2.41	   Removing the simple loops: 0 1.
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Accelerating simple loops of location 1.
4.89/2.41	
4.89/2.41	   Accelerating the following rules:
4.89/2.41	
4.89/2.41	      2: f21 -> f21 : [], cost: 1
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.89/2.41	
4.89/2.41	   Removing the simple loops: 2.
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Accelerated all simple loops using metering functions (where possible):
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	      4: f11 -> f21 : [ 0>=A ], cost: 1
4.89/2.41	
4.89/2.41	      6: f11 -> f11 : A'=-2*meter+A, B'=-meter+B, C'=meter+C, D'=free, [ A>=1 && free>=1 && 2*meter==A && meter>=1 ], cost: meter
4.89/2.41	
4.89/2.41	      7: f11 -> f11 : A'=-2*k+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B && k>0 && 2-2*k+A>=1 && 2-2*k+A>=1+B ], cost: k
4.89/2.41	
4.89/2.41	      8: f21 -> [6] : [], cost: INF
4.89/2.41	
4.89/2.41	      5: f0 -> f11 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Chained accelerated rules (with incoming rules):
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	      4: f11 -> f21 : [ 0>=A ], cost: 1
4.89/2.41	
4.89/2.41	     11: f11 -> [6] : [ 0>=A ], cost: INF
4.89/2.41	
4.89/2.41	      5: f0 -> f11 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.89/2.41	
4.89/2.41	      9: f0 -> f11 : A'=0, B'=-2+free_2, C'=2, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: 3
4.89/2.41	
4.89/2.41	     10: f0 -> f11 : A'=4-2*k, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 && k>0 && 6-2*k>=1 && 6-2*k>=1+free_2 ], cost: 1+k
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Removed unreachable locations (and leaf rules with constant cost):
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	     11: f11 -> [6] : [ 0>=A ], cost: INF
4.89/2.41	
4.89/2.41	      5: f0 -> f11 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.89/2.41	
4.89/2.41	      9: f0 -> f11 : A'=0, B'=-2+free_2, C'=2, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: 3
4.89/2.41	
4.89/2.41	     10: f0 -> f11 : A'=4-2*k, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 && k>0 && 6-2*k>=1 && 6-2*k>=1+free_2 ], cost: 1+k
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Eliminated locations (on tree-shaped paths):
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	     12: f0 -> [6] : A'=0, B'=-2+free_2, C'=2, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: INF
4.89/2.41	
4.89/2.41	     13: f0 -> [6] : A'=4-2*k, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 && k>0 && 6-2*k>=1 && 6-2*k>=1+free_2 && 0>=4-2*k ], cost: INF
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	### Computing asymptotic complexity ###
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Fully simplified ITS problem
4.89/2.41	
4.89/2.41	   Start location: f0
4.89/2.41	
4.89/2.41	     12: f0 -> [6] : A'=0, B'=-2+free_2, C'=2, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: INF
4.89/2.41	
4.89/2.41	     13: f0 -> [6] : A'=4-2*k, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 && k>0 && 6-2*k>=1 && 6-2*k>=1+free_2 && 0>=4-2*k ], cost: INF
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Computing asymptotic complexity for rule 12
4.89/2.41	
4.89/2.41	   Resulting cost INF has complexity: Nonterm
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Found new complexity Nonterm.
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	Obtained the following overall complexity (w.r.t. the length of the input n):
4.89/2.41	
4.89/2.41	   Complexity:  Nonterm
4.89/2.41	
4.89/2.41	   Cpx degree:  Nonterm
4.89/2.41	
4.89/2.41	   Solved cost: INF
4.89/2.41	
4.89/2.41	   Rule cost:   INF
4.89/2.41	
4.89/2.41	   Rule guard:  [ free_2>=1 && free>=1 ]
4.89/2.41	
4.89/2.41	
4.89/2.41	
4.89/2.41	NO
4.89/2.41	
4.89/2.41	
4.89/2.41	----------------------------------------
4.89/2.41	
4.89/2.41	(2)
4.89/2.41	BOUNDS(INF, INF)
4.89/2.45	EOF