6.51/2.85	WORST_CASE(NON_POLY, ?)
6.51/2.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.51/2.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.51/2.86	
6.51/2.86	
6.51/2.86	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
6.51/2.86	
6.51/2.86	(0) CpxIntTrs
6.51/2.86	(1) Loat Proof [FINISHED, 1131 ms]
6.51/2.86	(2) BOUNDS(INF, INF)
6.51/2.86	
6.51/2.86	
6.51/2.86	----------------------------------------
6.51/2.86	
6.51/2.86	(0)
6.51/2.86	Obligation:
6.51/2.86	Complexity Int TRS consisting of the following rules:
6.51/2.86	f0(A, B, C, D, E, F, G) -> Com_1(f6(8, 0, 14, -(1), E, F, G)) :|: TRUE
6.51/2.86	f6(A, B, C, D, E, F, G) -> Com_1(f12(A, B, C, D, I, F, G)) :|: C >= B && A >= H + 1
6.51/2.86	f6(A, B, C, D, E, F, G) -> Com_1(f12(A, B, C, D, I, F, G)) :|: C >= B
6.51/2.86	f6(A, B, C, D, E, F, G) -> Com_1(f6(A, B, B - 1, I, H, F, G)) :|: C >= B
6.51/2.86	f12(A, B, C, D, E, F, G) -> Com_1(f6(A, B, E - 1, D, E, F, G)) :|: TRUE
6.51/2.86	f12(A, B, C, D, E, F, G) -> Com_1(f6(A, E + 1, C, D, E, F, G)) :|: TRUE
6.51/2.86	f6(A, B, C, D, E, F, G) -> Com_1(f20(A, B, C, D, E, D, D)) :|: B >= 1 + C
6.51/2.86	
6.51/2.86	The start-symbols are:[f0_7]
6.51/2.86	
6.51/2.86	
6.51/2.86	----------------------------------------
6.51/2.86	
6.51/2.86	(1) Loat Proof (FINISHED)
6.51/2.86	
6.51/2.86	
6.51/2.86	### Pre-processing the ITS problem ###
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Initial linear ITS problem
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      1: f6 -> f12 : E'=free, [ C>=B && A>=1+free_1 ], cost: 1
6.51/2.86	
6.51/2.86	      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      6: f6 -> f20 : F'=D, G'=D, [ B>=1+C ], cost: 1
6.51/2.86	
6.51/2.86	      4: f12 -> f6 : C'=-1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      5: f12 -> f6 : B'=1+E, [], cost: 1
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Removed unreachable and leaf rules:
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      1: f6 -> f12 : E'=free, [ C>=B && A>=1+free_1 ], cost: 1
6.51/2.86	
6.51/2.86	      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      4: f12 -> f6 : C'=-1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      5: f12 -> f6 : B'=1+E, [], cost: 1
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Simplified all rules, resulting in:
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      4: f12 -> f6 : C'=-1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      5: f12 -> f6 : B'=1+E, [], cost: 1
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	### Simplification by acceleration and chaining ###
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Accelerating simple loops of location 1.
6.51/2.86	
6.51/2.86	   Accelerating the following rules:
6.51/2.86	
6.51/2.86	      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	   Found no metering function for rule 3.
6.51/2.86	
6.51/2.86	   Removing the simple loops:.
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Accelerated all simple loops using metering functions (where possible):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      4: f12 -> f6 : C'=-1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      5: f12 -> f6 : B'=1+E, [], cost: 1
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Chained accelerated rules (with incoming rules):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2
6.51/2.86	
6.51/2.86	      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1
6.51/2.86	
6.51/2.86	      4: f12 -> f6 : C'=-1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      5: f12 -> f6 : B'=1+E, [], cost: 1
6.51/2.86	
6.51/2.86	      8: f12 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ -1+E>=B ], cost: 2
6.51/2.86	
6.51/2.86	      9: f12 -> f6 : B'=1+E, C'=E, D'=free_3, E'=free_4, [ C>=1+E ], cost: 2
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Eliminated locations (on tree-shaped paths):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2
6.51/2.86	
6.51/2.86	     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     12: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B && -1+free>=B ], cost: 3
6.51/2.86	
6.51/2.86	     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3
6.51/2.86	
6.51/2.86	     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     16: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B && -1+free_2>=B ], cost: 3
6.51/2.86	
6.51/2.86	     17: f6 -> f6 : B'=1+free_2, C'=free_2, D'=free_3, E'=free_4, [ C>=B && C>=1+free_2 ], cost: 3
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Applied pruning (of leafs and parallel rules):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2
6.51/2.86	
6.51/2.86	     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3
6.51/2.86	
6.51/2.86	     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Accelerating simple loops of location 1.
6.51/2.86	
6.51/2.86	   Accelerating the following rules:
6.51/2.86	
6.51/2.86	     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3
6.51/2.86	
6.51/2.86	     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	   Accelerated rule 10 with NONTERM (after strengthening guard), yielding the new rule 18.
6.51/2.86	
6.51/2.86	   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 19.
6.51/2.86	
6.51/2.86	   Found no metering function for rule 13.
6.51/2.86	
6.51/2.86	   Accelerated rule 14 with NONTERM (after strengthening guard), yielding the new rule 20.
6.51/2.86	
6.51/2.86	   Accelerated rule 15 with NONTERM (after strengthening guard), yielding the new rule 21.
6.51/2.86	
6.51/2.86	   Removing the simple loops:.
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Accelerated all simple loops using metering functions (where possible):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2
6.51/2.86	
6.51/2.86	     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3
6.51/2.86	
6.51/2.86	     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2
6.51/2.86	
6.51/2.86	     18: f6 -> [5] : [ C>=B && -1+free>=B ], cost: INF
6.51/2.86	
6.51/2.86	     19: f6 -> [5] : [ C>=B && C>=1+free ], cost: INF
6.51/2.86	
6.51/2.86	     20: f6 -> [5] : [ C>=B && -1+free_2>=B ], cost: INF
6.51/2.86	
6.51/2.86	     21: f6 -> [5] : [ C>=B && C>=1+free_2 ], cost: INF
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Chained accelerated rules (with incoming rules):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1
6.51/2.86	
6.51/2.86	      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2
6.51/2.86	
6.51/2.86	     22: f0 -> f6 : A'=8, B'=0, C'=-1+free, D'=-1, E'=free, [], cost: 3
6.51/2.86	
6.51/2.86	     23: f0 -> f6 : A'=8, B'=1+free, C'=14, D'=-1, E'=free, [], cost: 3
6.51/2.86	
6.51/2.86	     24: f0 -> f6 : A'=8, B'=1+free, C'=free, D'=free_3, E'=free_4, [ 14>=1+free ], cost: 4
6.51/2.86	
6.51/2.86	     25: f0 -> f6 : A'=8, B'=0, C'=-1+free_2, D'=-1, E'=free_2, [], cost: 3
6.51/2.86	
6.51/2.86	     26: f0 -> f6 : A'=8, B'=1+free_2, C'=14, D'=-1, E'=free_2, [], cost: 3
6.51/2.86	
6.51/2.86	     27: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     28: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     29: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Removed unreachable locations (and leaf rules with constant cost):
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	     27: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     28: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     29: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	### Computing asymptotic complexity ###
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Fully simplified ITS problem
6.51/2.86	
6.51/2.86	   Start location: f0
6.51/2.86	
6.51/2.86	     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Computing asymptotic complexity for rule 30
6.51/2.86	
6.51/2.86	   Resulting cost INF has complexity: Nonterm
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Found new complexity Nonterm.
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	Obtained the following overall complexity (w.r.t. the length of the input n):
6.51/2.86	
6.51/2.86	   Complexity:  Nonterm
6.51/2.86	
6.51/2.86	   Cpx degree:  Nonterm
6.51/2.86	
6.51/2.86	   Solved cost: INF
6.51/2.86	
6.51/2.86	   Rule cost:   INF
6.51/2.86	
6.51/2.86	   Rule guard:  []
6.51/2.86	
6.51/2.86	
6.51/2.86	
6.51/2.86	NO
6.51/2.86	
6.51/2.86	
6.51/2.86	----------------------------------------
6.51/2.86	
6.51/2.86	(2)
6.51/2.86	BOUNDS(INF, INF)
6.51/2.88	EOF