4.94/2.30	WORST_CASE(NON_POLY, ?)
4.94/2.31	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.94/2.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.94/2.31	
4.94/2.31	
4.94/2.31	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.94/2.31	
4.94/2.31	(0) CpxIntTrs
4.94/2.31	(1) Loat Proof [FINISHED, 621 ms]
4.94/2.31	(2) BOUNDS(INF, INF)
4.94/2.31	
4.94/2.31	
4.94/2.31	----------------------------------------
4.94/2.31	
4.94/2.31	(0)
4.94/2.31	Obligation:
4.94/2.31	Complexity Int TRS consisting of the following rules:
4.94/2.31	f12(A, B, C, D, E, F) -> Com_1(f12(A - 1, B - 1, C + 1, G, E, F)) :|: A >= 1 && G >= 1
4.94/2.31	f12(A, B, C, D, E, F) -> Com_1(f12(A - 1, B, C, G, E, F)) :|: 0 >= G && A >= 1 && A >= B + 1
4.94/2.31	f22(A, B, C, D, E, F) -> Com_1(f22(A, B, C, D, E, F)) :|: TRUE
4.94/2.31	f24(A, B, C, D, E, F) -> Com_1(f27(A, B, C, D, E, F)) :|: TRUE
4.94/2.31	f12(A, B, C, D, E, F) -> Com_1(f22(A, B, C, D, E, F)) :|: 0 >= A
4.94/2.31	f0(A, B, C, D, E, F) -> Com_1(f12(4, G, 0, D, G, 4)) :|: G >= 1
4.94/2.31	
4.94/2.31	The start-symbols are:[f0_6]
4.94/2.31	
4.94/2.31	
4.94/2.31	----------------------------------------
4.94/2.31	
4.94/2.31	(1) Loat Proof (FINISHED)
4.94/2.31	
4.94/2.31	
4.94/2.31	### Pre-processing the ITS problem ###
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Initial linear ITS problem
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	      0: f12 -> f12 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.94/2.31	
4.94/2.31	      1: f12 -> f12 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.94/2.31	
4.94/2.31	      4: f12 -> f22 : [ 0>=A ], cost: 1
4.94/2.31	
4.94/2.31	      2: f22 -> f22 : [], cost: 1
4.94/2.31	
4.94/2.31	      3: f24 -> f27 : [], cost: 1
4.94/2.31	
4.94/2.31	      5: f0 -> f12 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Removed unreachable and leaf rules:
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	      0: f12 -> f12 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.94/2.31	
4.94/2.31	      1: f12 -> f12 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.94/2.31	
4.94/2.31	      4: f12 -> f22 : [ 0>=A ], cost: 1
4.94/2.31	
4.94/2.31	      2: f22 -> f22 : [], cost: 1
4.94/2.31	
4.94/2.31	      5: f0 -> f12 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	### Simplification by acceleration and chaining ###
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Accelerating simple loops of location 0.
4.94/2.31	
4.94/2.31	   Accelerating the following rules:
4.94/2.31	
4.94/2.31	      0: f12 -> f12 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
4.94/2.31	
4.94/2.31	      1: f12 -> f12 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	   Accelerated rule 0 with metering function A, yielding the new rule 6.
4.94/2.31	
4.94/2.31	   Accelerated rule 1 with backward acceleration, yielding the new rule 7.
4.94/2.31	
4.94/2.31	   Accelerated rule 1 with backward acceleration, yielding the new rule 8.
4.94/2.31	
4.94/2.31	   Removing the simple loops: 0 1.
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Accelerating simple loops of location 1.
4.94/2.31	
4.94/2.31	   Accelerating the following rules:
4.94/2.31	
4.94/2.31	      2: f22 -> f22 : [], cost: 1
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	   Accelerated rule 2 with NONTERM, yielding the new rule 9.
4.94/2.31	
4.94/2.31	   Removing the simple loops: 2.
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Accelerated all simple loops using metering functions (where possible):
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	      4: f12 -> f22 : [ 0>=A ], cost: 1
4.94/2.31	
4.94/2.31	      6: f12 -> f12 : A'=0, B'=-A+B, C'=C+A, D'=free, [ A>=1 && free>=1 ], cost: A
4.94/2.31	
4.94/2.31	      7: f12 -> f12 : A'=0, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B && 1>=1+B ], cost: A
4.94/2.31	
4.94/2.31	      8: f12 -> f12 : A'=B, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B && 1+B>=1 ], cost: A-B
4.94/2.31	
4.94/2.31	      9: f22 -> [6] : [], cost: INF
4.94/2.31	
4.94/2.31	      5: f0 -> f12 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Chained accelerated rules (with incoming rules):
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	      4: f12 -> f22 : [ 0>=A ], cost: 1
4.94/2.31	
4.94/2.31	     12: f12 -> [6] : [ 0>=A ], cost: INF
4.94/2.31	
4.94/2.31	      5: f0 -> f12 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.94/2.31	
4.94/2.31	     10: f0 -> f12 : A'=0, B'=-4+free_2, C'=4, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: 5
4.94/2.31	
4.94/2.31	     11: f0 -> f12 : A'=free_2, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 ], cost: 5-free_2
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Removed unreachable locations (and leaf rules with constant cost):
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	     12: f12 -> [6] : [ 0>=A ], cost: INF
4.94/2.31	
4.94/2.31	      5: f0 -> f12 : A'=4, B'=free_2, C'=0, E'=free_2, F'=4, [ free_2>=1 ], cost: 1
4.94/2.31	
4.94/2.31	     10: f0 -> f12 : A'=0, B'=-4+free_2, C'=4, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: 5
4.94/2.31	
4.94/2.31	     11: f0 -> f12 : A'=free_2, B'=free_2, C'=0, D'=free_1, E'=free_2, F'=4, [ free_2>=1 && 0>=free_1 && 4>=1+free_2 ], cost: 5-free_2
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Eliminated locations (on tree-shaped paths):
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	     13: f0 -> [6] : A'=0, B'=-4+free_2, C'=4, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: INF
4.94/2.31	
4.94/2.31	     14: f0 -> [7] : [ free_2>=1 && 0>=free_1 && 4>=1+free_2 ], cost: 5-free_2
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	### Computing asymptotic complexity ###
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Fully simplified ITS problem
4.94/2.31	
4.94/2.31	   Start location: f0
4.94/2.31	
4.94/2.31	     13: f0 -> [6] : A'=0, B'=-4+free_2, C'=4, D'=free, E'=free_2, F'=4, [ free_2>=1 && free>=1 ], cost: INF
4.94/2.31	
4.94/2.31	     14: f0 -> [7] : [ free_2>=1 && 0>=free_1 && 4>=1+free_2 ], cost: 5-free_2
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Computing asymptotic complexity for rule 13
4.94/2.31	
4.94/2.31	   Resulting cost INF has complexity: Nonterm
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Found new complexity Nonterm.
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	Obtained the following overall complexity (w.r.t. the length of the input n):
4.94/2.31	
4.94/2.31	   Complexity:  Nonterm
4.94/2.31	
4.94/2.31	   Cpx degree:  Nonterm
4.94/2.31	
4.94/2.31	   Solved cost: INF
4.94/2.31	
4.94/2.31	   Rule cost:   INF
4.94/2.31	
4.94/2.31	   Rule guard:  [ free_2>=1 && free>=1 ]
4.94/2.31	
4.94/2.31	
4.94/2.31	
4.94/2.31	NO
4.94/2.31	
4.94/2.31	
4.94/2.31	----------------------------------------
4.94/2.31	
4.94/2.31	(2)
4.94/2.31	BOUNDS(INF, INF)
4.94/2.33	EOF