3.51/1.89	WORST_CASE(NON_POLY, ?)
3.51/1.90	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.51/1.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.51/1.90	
3.51/1.90	
3.51/1.90	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.51/1.90	
3.51/1.90	(0) CpxIntTrs
3.51/1.90	(1) Loat Proof [FINISHED, 132 ms]
3.51/1.90	(2) BOUNDS(INF, INF)
3.51/1.90	
3.51/1.90	
3.51/1.90	----------------------------------------
3.51/1.90	
3.51/1.90	(0)
3.51/1.90	Obligation:
3.51/1.90	Complexity Int TRS consisting of the following rules:
3.51/1.90	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, L, M, N, F, F, G, H, I, J, K)) :|: A >= 2
3.51/1.90	f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, L, M, D, E, F, N, H, I, J, K)) :|: 1 >= A
3.51/1.90	f300(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, L, M, N, O, O, G, H, P, Q, R)) :|: H >= 1
3.51/1.90	f300(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, L, M, D, N, P, O, H, Q, N, R)) :|: 0 >= H
3.51/1.90	
3.51/1.90	The start-symbols are:[f300_11]
3.51/1.90	
3.51/1.90	
3.51/1.90	----------------------------------------
3.51/1.90	
3.51/1.90	(1) Loat Proof (FINISHED)
3.51/1.90	
3.51/1.90	
3.51/1.90	### Pre-processing the ITS problem ###
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Initial linear ITS problem
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      0: f2 -> f2 : B'=free, C'=free_1, D'=free_2, E'=F, [ A>=2 ], cost: 1
3.51/1.90	
3.51/1.90	      1: f2 -> f1 : B'=free_3, C'=free_4, G'=free_5, [ 1>=A ], cost: 1
3.51/1.90	
3.51/1.90	      2: f300 -> f2 : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 ], cost: 1
3.51/1.90	
3.51/1.90	      3: f300 -> f1 : B'=free_13, C'=free_15, E'=free_17, F'=free_19, G'=free_14, Q'=free_16, J'=free_17, K'=free_18, [ 0>=H ], cost: 1
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Removed unreachable and leaf rules:
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      0: f2 -> f2 : B'=free, C'=free_1, D'=free_2, E'=F, [ A>=2 ], cost: 1
3.51/1.90	
3.51/1.90	      2: f300 -> f2 : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 ], cost: 1
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	### Simplification by acceleration and chaining ###
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Accelerating simple loops of location 0.
3.51/1.90	
3.51/1.90	   Accelerating the following rules:
3.51/1.90	
3.51/1.90	      0: f2 -> f2 : B'=free, C'=free_1, D'=free_2, E'=F, [ A>=2 ], cost: 1
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	   Accelerated rule 0 with NONTERM, yielding the new rule 4.
3.51/1.90	
3.51/1.90	   Removing the simple loops: 0.
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Accelerated all simple loops using metering functions (where possible):
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      4: f2 -> [3] : [ A>=2 ], cost: INF
3.51/1.90	
3.51/1.90	      2: f300 -> f2 : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 ], cost: 1
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Chained accelerated rules (with incoming rules):
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      2: f300 -> f2 : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 ], cost: 1
3.51/1.90	
3.51/1.90	      5: f300 -> [3] : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 && A>=2 ], cost: INF
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Removed unreachable locations (and leaf rules with constant cost):
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      5: f300 -> [3] : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 && A>=2 ], cost: INF
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	### Computing asymptotic complexity ###
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Fully simplified ITS problem
3.51/1.90	
3.51/1.90	   Start location: f300
3.51/1.90	
3.51/1.90	      5: f300 -> [3] : B'=free_6, C'=free_8, D'=free_10, E'=free_12, F'=free_12, Q'=free_7, J'=free_9, K'=free_11, [ H>=1 && A>=2 ], cost: INF
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Computing asymptotic complexity for rule 5
3.51/1.90	
3.51/1.90	   Resulting cost INF has complexity: Nonterm
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Found new complexity Nonterm.
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	Obtained the following overall complexity (w.r.t. the length of the input n):
3.51/1.90	
3.51/1.90	   Complexity:  Nonterm
3.51/1.90	
3.51/1.90	   Cpx degree:  Nonterm
3.51/1.90	
3.51/1.90	   Solved cost: INF
3.51/1.90	
3.51/1.90	   Rule cost:   INF
3.51/1.90	
3.51/1.90	   Rule guard:  [ H>=1 && A>=2 ]
3.51/1.90	
3.51/1.90	
3.51/1.90	
3.51/1.90	NO
3.51/1.90	
3.51/1.90	
3.51/1.90	----------------------------------------
3.51/1.90	
3.51/1.90	(2)
3.51/1.90	BOUNDS(INF, INF)
3.87/1.96	EOF