3.98/1.89	WORST_CASE(NON_POLY, ?)
3.98/1.89	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.98/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.98/1.89	
3.98/1.89	
3.98/1.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.98/1.89	
3.98/1.89	(0) CpxIntTrs
3.98/1.89	(1) Loat Proof [FINISHED, 222 ms]
3.98/1.89	(2) BOUNDS(INF, INF)
3.98/1.89	
3.98/1.89	
3.98/1.89	----------------------------------------
3.98/1.89	
3.98/1.89	(0)
3.98/1.89	Obligation:
3.98/1.89	Complexity Int TRS consisting of the following rules:
3.98/1.89	f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, J, M, G, H, I)) :|: J >= 1 && B >= 1 + A
3.98/1.89	f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, J, M, G, H, I)) :|: 0 >= J + 1 && B >= 1 + A
3.98/1.89	f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, 0, F, G, H, I)) :|: B >= 1 + A
3.98/1.89	f1(A, B, C, D, E, F, G, H, I) -> Com_1(f300(A, B, K, L, E, F, J, H, I)) :|: A >= B
3.98/1.89	f2(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, C, D, E, F, G, K, L)) :|: TRUE
3.98/1.89	
3.98/1.89	The start-symbols are:[f2_9]
3.98/1.89	
3.98/1.89	
3.98/1.89	----------------------------------------
3.98/1.89	
3.98/1.89	(1) Loat Proof (FINISHED)
3.98/1.89	
3.98/1.89	
3.98/1.89	### Pre-processing the ITS problem ###
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Initial linear ITS problem
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	      0: f1 -> f1 : C'=free_3, D'=free, E'=free_2, F'=free_1, [ free_2>=1 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      1: f1 -> f1 : C'=free_7, D'=free_4, E'=free_6, F'=free_5, [ 0>=1+free_6 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      2: f1 -> f1 : C'=free_9, D'=free_8, E'=0, [ A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      3: f1 -> f300 : C'=free_12, D'=free_10, G'=free_11, [ B>=A ], cost: 1
3.98/1.89	
3.98/1.89	      4: f2 -> f1 : H'=free_14, Q'=free_13, [], cost: 1
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Removed unreachable and leaf rules:
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	      0: f1 -> f1 : C'=free_3, D'=free, E'=free_2, F'=free_1, [ free_2>=1 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      1: f1 -> f1 : C'=free_7, D'=free_4, E'=free_6, F'=free_5, [ 0>=1+free_6 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      2: f1 -> f1 : C'=free_9, D'=free_8, E'=0, [ A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      4: f2 -> f1 : H'=free_14, Q'=free_13, [], cost: 1
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	### Simplification by acceleration and chaining ###
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Accelerating simple loops of location 0.
3.98/1.89	
3.98/1.89	   Accelerating the following rules:
3.98/1.89	
3.98/1.89	      0: f1 -> f1 : C'=free_3, D'=free, E'=free_2, F'=free_1, [ free_2>=1 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      1: f1 -> f1 : C'=free_7, D'=free_4, E'=free_6, F'=free_5, [ 0>=1+free_6 && A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	      2: f1 -> f1 : C'=free_9, D'=free_8, E'=0, [ A>=1+B ], cost: 1
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	   Accelerated rule 0 with NONTERM, yielding the new rule 5.
3.98/1.89	
3.98/1.89	   Accelerated rule 1 with NONTERM, yielding the new rule 6.
3.98/1.89	
3.98/1.89	   Accelerated rule 2 with NONTERM, yielding the new rule 7.
3.98/1.89	
3.98/1.89	   Removing the simple loops: 0 1 2.
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Accelerated all simple loops using metering functions (where possible):
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	      5: f1 -> [3] : [ free_2>=1 && A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	      6: f1 -> [3] : [ 0>=1+free_6 && A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	      7: f1 -> [3] : [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	      4: f2 -> f1 : H'=free_14, Q'=free_13, [], cost: 1
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Chained accelerated rules (with incoming rules):
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	      4: f2 -> f1 : H'=free_14, Q'=free_13, [], cost: 1
3.98/1.89	
3.98/1.89	      8: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	      9: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	     10: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Removed unreachable locations (and leaf rules with constant cost):
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	      8: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	      9: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	     10: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	### Computing asymptotic complexity ###
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Fully simplified ITS problem
3.98/1.89	
3.98/1.89	   Start location: f2
3.98/1.89	
3.98/1.89	     10: f2 -> [3] : H'=free_14, Q'=free_13, [ A>=1+B ], cost: INF
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Computing asymptotic complexity for rule 10
3.98/1.89	
3.98/1.89	   Resulting cost INF has complexity: Nonterm
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Found new complexity Nonterm.
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	Obtained the following overall complexity (w.r.t. the length of the input n):
3.98/1.89	
3.98/1.89	   Complexity:  Nonterm
3.98/1.89	
3.98/1.89	   Cpx degree:  Nonterm
3.98/1.89	
3.98/1.89	   Solved cost: INF
3.98/1.89	
3.98/1.89	   Rule cost:   INF
3.98/1.89	
3.98/1.89	   Rule guard:  [ A>=1+B ]
3.98/1.89	
3.98/1.89	
3.98/1.89	
3.98/1.89	NO
3.98/1.89	
3.98/1.89	
3.98/1.89	----------------------------------------
3.98/1.89	
3.98/1.89	(2)
3.98/1.89	BOUNDS(INF, INF)
4.02/1.91	EOF