3.94/1.77	WORST_CASE(NON_POLY, ?)
3.94/1.78	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.94/1.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.94/1.78	
3.94/1.78	
3.94/1.78	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.94/1.78	
3.94/1.78	(0) CpxIntTrs
3.94/1.78	(1) Loat Proof [FINISHED, 100 ms]
3.94/1.78	(2) BOUNDS(INF, INF)
3.94/1.78	
3.94/1.78	
3.94/1.78	----------------------------------------
3.94/1.78	
3.94/1.78	(0)
3.94/1.78	Obligation:
3.94/1.78	Complexity Int TRS consisting of the following rules:
3.94/1.78	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, C, C, L, M, N, G, H, I, J, K)) :|: A >= 1
3.94/1.78	f300(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, L, N, P, Q, F, G, L, M, O, R)) :|: 0 >= G
3.94/1.78	f300(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, N, N, P, Q, R, G, L, M, O, K)) :|: A >= 1 && G >= 1
3.94/1.78	f300(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, N, N, P, Q, R, G, L, M, O, S)) :|: 0 >= A && G >= 1
3.94/1.78	
3.94/1.78	The start-symbols are:[f300_11]
3.94/1.78	
3.94/1.78	
3.94/1.78	----------------------------------------
3.94/1.78	
3.94/1.78	(1) Loat Proof (FINISHED)
3.94/1.78	
3.94/1.78	
3.94/1.78	### Pre-processing the ITS problem ###
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Initial linear ITS problem
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      0: f2 -> f2 : B'=C, D'=free, E'=free_1, F'=free_2, [ A>=1 ], cost: 1
3.94/1.78	
3.94/1.78	      1: f300 -> f1 : B'=free_3, C'=free_5, D'=free_7, E'=free_9, H'=free_3, Q'=free_4, J'=free_6, K'=free_8, [ 0>=G ], cost: 1
3.94/1.78	
3.94/1.78	      2: f300 -> f2 : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: 1
3.94/1.78	
3.94/1.78	      3: f300 -> f1 : B'=free_17, C'=free_17, D'=free_20, E'=free_22, F'=free_24, H'=free_19, Q'=free_21, J'=free_23, K'=free_18, [ 0>=A && G>=1 ], cost: 1
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Removed unreachable and leaf rules:
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      0: f2 -> f2 : B'=C, D'=free, E'=free_1, F'=free_2, [ A>=1 ], cost: 1
3.94/1.78	
3.94/1.78	      2: f300 -> f2 : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: 1
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	### Simplification by acceleration and chaining ###
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Accelerating simple loops of location 0.
3.94/1.78	
3.94/1.78	   Accelerating the following rules:
3.94/1.78	
3.94/1.78	      0: f2 -> f2 : B'=C, D'=free, E'=free_1, F'=free_2, [ A>=1 ], cost: 1
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	   Accelerated rule 0 with NONTERM, yielding the new rule 4.
3.94/1.78	
3.94/1.78	   Removing the simple loops: 0.
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Accelerated all simple loops using metering functions (where possible):
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      4: f2 -> [3] : [ A>=1 ], cost: INF
3.94/1.78	
3.94/1.78	      2: f300 -> f2 : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: 1
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Chained accelerated rules (with incoming rules):
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      2: f300 -> f2 : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: 1
3.94/1.78	
3.94/1.78	      5: f300 -> [3] : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: INF
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Removed unreachable locations (and leaf rules with constant cost):
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      5: f300 -> [3] : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: INF
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	### Computing asymptotic complexity ###
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Fully simplified ITS problem
3.94/1.78	
3.94/1.78	   Start location: f300
3.94/1.78	
3.94/1.78	      5: f300 -> [3] : B'=free_10, C'=free_10, D'=free_12, E'=free_14, F'=free_16, H'=free_11, Q'=free_13, J'=free_15, [ A>=1 && G>=1 ], cost: INF
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Computing asymptotic complexity for rule 5
3.94/1.78	
3.94/1.78	   Resulting cost INF has complexity: Nonterm
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Found new complexity Nonterm.
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	Obtained the following overall complexity (w.r.t. the length of the input n):
3.94/1.78	
3.94/1.78	   Complexity:  Nonterm
3.94/1.78	
3.94/1.78	   Cpx degree:  Nonterm
3.94/1.78	
3.94/1.78	   Solved cost: INF
3.94/1.78	
3.94/1.78	   Rule cost:   INF
3.94/1.78	
3.94/1.78	   Rule guard:  [ A>=1 && G>=1 ]
3.94/1.78	
3.94/1.78	
3.94/1.78	
3.94/1.78	NO
3.94/1.78	
3.94/1.78	
3.94/1.78	----------------------------------------
3.94/1.78	
3.94/1.78	(2)
3.94/1.78	BOUNDS(INF, INF)
3.94/1.80	EOF