5.83/2.46	WORST_CASE(NON_POLY, ?)
5.83/2.47	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.83/2.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.83/2.47	
5.83/2.47	
5.83/2.47	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
5.83/2.47	
5.83/2.47	(0) CpxIntTrs
5.83/2.47	(1) Loat Proof [FINISHED, 830 ms]
5.83/2.47	(2) BOUNDS(INF, INF)
5.83/2.47	
5.83/2.47	
5.83/2.47	----------------------------------------
5.83/2.47	
5.83/2.47	(0)
5.83/2.47	Obligation:
5.83/2.47	Complexity Int TRS consisting of the following rules:
5.83/2.47	f0(A, B, C, D, E) -> Com_1(f3(0, 0, C, D, E)) :|: TRUE
5.83/2.47	f3(A, B, C, D, E) -> Com_1(f3(A, B, C - 1, F, E)) :|: C >= 1 && F >= 1
5.83/2.47	f3(A, B, C, D, E) -> Com_1(f3(A, B, C - 2, F, E)) :|: C >= 1 && 0 >= F
5.83/2.47	f3(A, B, C, D, E) -> Com_1(f6(A, B, C, D, F)) :|: 0 >= C
5.83/2.47	f6(A, B, C, D, E) -> Com_1(f6(1, B, C, D, F)) :|: E >= 1
5.83/2.47	f6(A, B, C, D, E) -> Com_1(f6(0, B, C, D, F)) :|: 0 >= E
5.83/2.47	
5.83/2.47	The start-symbols are:[f0_5]
5.83/2.47	
5.83/2.47	
5.83/2.47	----------------------------------------
5.83/2.47	
5.83/2.47	(1) Loat Proof (FINISHED)
5.83/2.47	
5.83/2.47	
5.83/2.47	### Pre-processing the ITS problem ###
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Initial linear ITS problem
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	      0: f0 -> f3 : A'=0, B'=0, [], cost: 1
5.83/2.47	
5.83/2.47	      1: f3 -> f3 : C'=-1+C, D'=free, [ C>=1 && free>=1 ], cost: 1
5.83/2.47	
5.83/2.47	      2: f3 -> f3 : C'=-2+C, D'=free_1, [ C>=1 && 0>=free_1 ], cost: 1
5.83/2.47	
5.83/2.47	      3: f3 -> f6 : E'=free_2, [ 0>=C ], cost: 1
5.83/2.47	
5.83/2.47	      4: f6 -> f6 : A'=1, E'=free_3, [ E>=1 ], cost: 1
5.83/2.47	
5.83/2.47	      5: f6 -> f6 : A'=0, E'=free_4, [ 0>=E ], cost: 1
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	### Simplification by acceleration and chaining ###
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Accelerating simple loops of location 1.
5.83/2.47	
5.83/2.47	   Accelerating the following rules:
5.83/2.47	
5.83/2.47	      1: f3 -> f3 : C'=-1+C, D'=free, [ C>=1 && free>=1 ], cost: 1
5.83/2.47	
5.83/2.47	      2: f3 -> f3 : C'=-2+C, D'=free_1, [ C>=1 && 0>=free_1 ], cost: 1
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	   Accelerated rule 1 with metering function C, yielding the new rule 6.
5.83/2.47	
5.83/2.47	   Accelerated rule 2 with metering function meter (where 2*meter==C), yielding the new rule 7.
5.83/2.47	
5.83/2.47	      During metering: Instantiating temporary variables by {meter==1}
5.83/2.47	
5.83/2.47	   Removing the simple loops: 1 2.
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Accelerating simple loops of location 2.
5.83/2.47	
5.83/2.47	   Accelerating the following rules:
5.83/2.47	
5.83/2.47	      4: f6 -> f6 : A'=1, E'=free_3, [ E>=1 ], cost: 1
5.83/2.47	
5.83/2.47	      5: f6 -> f6 : A'=0, E'=free_4, [ 0>=E ], cost: 1
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	   Accelerated rule 4 with NONTERM (after strengthening guard), yielding the new rule 8.
5.83/2.47	
5.83/2.47	   Accelerated rule 5 with NONTERM (after strengthening guard), yielding the new rule 9.
5.83/2.47	
5.83/2.47	   Removing the simple loops:.
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Accelerated all simple loops using metering functions (where possible):
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	      0: f0 -> f3 : A'=0, B'=0, [], cost: 1
5.83/2.47	
5.83/2.47	      3: f3 -> f6 : E'=free_2, [ 0>=C ], cost: 1
5.83/2.47	
5.83/2.47	      6: f3 -> f3 : C'=0, D'=free, [ C>=1 && free>=1 ], cost: C
5.83/2.47	
5.83/2.47	      7: f3 -> f3 : C'=C-2*meter, D'=free_1, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 ], cost: meter
5.83/2.47	
5.83/2.47	      4: f6 -> f6 : A'=1, E'=free_3, [ E>=1 ], cost: 1
5.83/2.47	
5.83/2.47	      5: f6 -> f6 : A'=0, E'=free_4, [ 0>=E ], cost: 1
5.83/2.47	
5.83/2.47	      8: f6 -> [4] : [ E>=1 && free_3>=1 ], cost: INF
5.83/2.47	
5.83/2.47	      9: f6 -> [4] : [ 0>=E && 0>=free_4 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Chained accelerated rules (with incoming rules):
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	      0: f0 -> f3 : A'=0, B'=0, [], cost: 1
5.83/2.47	
5.83/2.47	     10: f0 -> f3 : A'=0, B'=0, C'=0, D'=free, [ C>=1 && free>=1 ], cost: 1+C
5.83/2.47	
5.83/2.47	     11: f0 -> f3 : A'=0, B'=0, C'=C-2*meter, D'=free_1, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 ], cost: 1+meter
5.83/2.47	
5.83/2.47	      3: f3 -> f6 : E'=free_2, [ 0>=C ], cost: 1
5.83/2.47	
5.83/2.47	     12: f3 -> f6 : A'=1, E'=free_3, [ 0>=C ], cost: 2
5.83/2.47	
5.83/2.47	     13: f3 -> f6 : A'=0, E'=free_4, [ 0>=C ], cost: 2
5.83/2.47	
5.83/2.47	     14: f3 -> [4] : E'=free_2, [ 0>=C && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     15: f3 -> [4] : E'=free_2, [ 0>=C && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Removed unreachable locations (and leaf rules with constant cost):
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	      0: f0 -> f3 : A'=0, B'=0, [], cost: 1
5.83/2.47	
5.83/2.47	     10: f0 -> f3 : A'=0, B'=0, C'=0, D'=free, [ C>=1 && free>=1 ], cost: 1+C
5.83/2.47	
5.83/2.47	     11: f0 -> f3 : A'=0, B'=0, C'=C-2*meter, D'=free_1, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 ], cost: 1+meter
5.83/2.47	
5.83/2.47	     14: f3 -> [4] : E'=free_2, [ 0>=C && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     15: f3 -> [4] : E'=free_2, [ 0>=C && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Eliminated locations (on tree-shaped paths):
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	     16: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     17: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     18: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     19: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     20: f0 -> [4] : A'=0, B'=0, C'=C-2*meter, D'=free_1, E'=free_2, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     21: f0 -> [4] : A'=0, B'=0, C'=C-2*meter, D'=free_1, E'=free_2, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Applied pruning (of leafs and parallel rules):
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	     16: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     17: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     18: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     19: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     21: f0 -> [4] : A'=0, B'=0, C'=C-2*meter, D'=free_1, E'=free_2, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	### Computing asymptotic complexity ###
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Fully simplified ITS problem
5.83/2.47	
5.83/2.47	   Start location: f0
5.83/2.47	
5.83/2.47	     16: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     17: f0 -> [4] : A'=0, B'=0, E'=free_2, [ 0>=C && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     18: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && free_2>=1 ], cost: INF
5.83/2.47	
5.83/2.47	     19: f0 -> [4] : A'=0, B'=0, C'=0, D'=free, E'=free_2, [ C>=1 && free>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	     21: f0 -> [4] : A'=0, B'=0, C'=C-2*meter, D'=free_1, E'=free_2, [ C>=1 && 0>=free_1 && 2*meter==C && meter>=1 && 0>=free_2 ], cost: INF
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Computing asymptotic complexity for rule 16
5.83/2.47	
5.83/2.47	   Resulting cost INF has complexity: Nonterm
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Found new complexity Nonterm.
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	Obtained the following overall complexity (w.r.t. the length of the input n):
5.83/2.47	
5.83/2.47	   Complexity:  Nonterm
5.83/2.47	
5.83/2.47	   Cpx degree:  Nonterm
5.83/2.47	
5.83/2.47	   Solved cost: INF
5.83/2.47	
5.83/2.47	   Rule cost:   INF
5.83/2.47	
5.83/2.47	   Rule guard:  [ 0>=C && free_2>=1 ]
5.83/2.47	
5.83/2.47	
5.83/2.47	
5.83/2.47	NO
5.83/2.47	
5.83/2.47	
5.83/2.47	----------------------------------------
5.83/2.47	
5.83/2.47	(2)
5.83/2.47	BOUNDS(INF, INF)
5.89/2.50	EOF