3.71/1.95	WORST_CASE(NON_POLY, ?)
3.71/1.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.71/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.71/1.96	
3.71/1.96	
3.71/1.96	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.71/1.96	
3.71/1.96	(0) CpxIntTrs
3.71/1.96	(1) Loat Proof [FINISHED, 242 ms]
3.71/1.96	(2) BOUNDS(INF, INF)
3.71/1.96	
3.71/1.96	
3.71/1.96	----------------------------------------
3.71/1.96	
3.71/1.96	(0)
3.71/1.96	Obligation:
3.71/1.96	Complexity Int TRS consisting of the following rules:
3.71/1.96	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, L, O, G, H, I, J, K)) :|: L >= 1 && B >= 1 + A
3.71/1.96	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, L, O, G, H, I, J, K)) :|: 0 >= L + 1 && B >= 1 + A
3.71/1.96	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, 0, F, G, H, I, J, K)) :|: B >= 1 + A
3.71/1.96	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f300(A, B, M, N, E, F, L, H, I, J, K)) :|: A >= B
3.71/1.96	f1(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, C, D, E, F, G, M, N, N, M)) :|: TRUE
3.71/1.96	
3.71/1.96	The start-symbols are:[f1_11]
3.71/1.96	
3.71/1.96	
3.71/1.96	----------------------------------------
3.71/1.96	
3.71/1.96	(1) Loat Proof (FINISHED)
3.71/1.96	
3.71/1.96	
3.71/1.96	### Pre-processing the ITS problem ###
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Initial linear ITS problem
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	      0: f2 -> f2 : C'=free_1, D'=free_2, E'=free, F'=free_3, [ free>=1 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      1: f2 -> f2 : C'=free_5, D'=free_6, E'=free_4, F'=free_7, [ 0>=1+free_4 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      2: f2 -> f2 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      3: f2 -> f300 : C'=free_11, D'=free_12, G'=free_10, [ B>=A ], cost: 1
3.71/1.96	
3.71/1.96	      4: f1 -> f2 : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [], cost: 1
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Removed unreachable and leaf rules:
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	      0: f2 -> f2 : C'=free_1, D'=free_2, E'=free, F'=free_3, [ free>=1 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      1: f2 -> f2 : C'=free_5, D'=free_6, E'=free_4, F'=free_7, [ 0>=1+free_4 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      2: f2 -> f2 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      4: f1 -> f2 : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [], cost: 1
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	### Simplification by acceleration and chaining ###
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Accelerating simple loops of location 0.
3.71/1.96	
3.71/1.96	   Accelerating the following rules:
3.71/1.96	
3.71/1.96	      0: f2 -> f2 : C'=free_1, D'=free_2, E'=free, F'=free_3, [ free>=1 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      1: f2 -> f2 : C'=free_5, D'=free_6, E'=free_4, F'=free_7, [ 0>=1+free_4 && A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	      2: f2 -> f2 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	   Accelerated rule 0 with NONTERM, yielding the new rule 5.
3.71/1.96	
3.71/1.96	   Accelerated rule 1 with NONTERM, yielding the new rule 6.
3.71/1.96	
3.71/1.96	   Accelerated rule 2 with NONTERM, yielding the new rule 7.
3.71/1.96	
3.71/1.96	   Removing the simple loops: 0 1 2.
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Accelerated all simple loops using metering functions (where possible):
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	      5: f2 -> [3] : [ free>=1 && A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	      6: f2 -> [3] : [ 0>=1+free_4 && A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	      7: f2 -> [3] : [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	      4: f1 -> f2 : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [], cost: 1
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Chained accelerated rules (with incoming rules):
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	      4: f1 -> f2 : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [], cost: 1
3.71/1.96	
3.71/1.96	      8: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	      9: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Removed unreachable locations (and leaf rules with constant cost):
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	      8: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	      9: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	### Computing asymptotic complexity ###
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Fully simplified ITS problem
3.71/1.96	
3.71/1.96	   Start location: f1
3.71/1.96	
3.71/1.96	     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: INF
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Computing asymptotic complexity for rule 10
3.71/1.96	
3.71/1.96	   Resulting cost INF has complexity: Nonterm
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Found new complexity Nonterm.
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Obtained the following overall complexity (w.r.t. the length of the input n):
3.71/1.96	
3.71/1.96	   Complexity:  Nonterm
3.71/1.96	
3.71/1.96	   Cpx degree:  Nonterm
3.71/1.96	
3.71/1.96	   Solved cost: INF
3.71/1.96	
3.71/1.96	   Rule cost:   INF
3.71/1.96	
3.71/1.96	   Rule guard:  [ A>=1+B ]
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	NO
3.71/1.96	
3.71/1.96	
3.71/1.96	----------------------------------------
3.71/1.96	
3.71/1.96	(2)
3.71/1.96	BOUNDS(INF, INF)
3.71/1.98	EOF