4.34/2.14	WORST_CASE(NON_POLY, ?)
4.34/2.15	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.34/2.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.34/2.15	
4.34/2.15	
4.34/2.15	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.34/2.15	
4.34/2.15	(0) CpxIntTrs
4.34/2.15	(1) Loat Proof [FINISHED, 427 ms]
4.34/2.15	(2) BOUNDS(INF, INF)
4.34/2.15	
4.34/2.15	
4.34/2.15	----------------------------------------
4.34/2.15	
4.34/2.15	(0)
4.34/2.15	Obligation:
4.34/2.15	Complexity Int TRS consisting of the following rules:
4.34/2.15	f0(A, B, C, D, E, F, G) -> Com_1(f2(H, B, I, D, E, F, G)) :|: A >= B
4.34/2.15	f0(A, B, C, D, E, F, G) -> Com_1(f0(H, B, C, I, 0, F, G)) :|: B >= A + 1
4.34/2.15	f0(A, B, C, D, E, F, G) -> Com_1(f0(H, B, C, I, J, K, G)) :|: 0 >= J + 1 && B >= A + 1
4.34/2.15	f0(A, B, C, D, E, F, G) -> Com_1(f0(H, B, C, I, J, K, G)) :|: J >= 1 && B >= A + 1
4.34/2.15	f1(A, B, C, D, E, F, G) -> Com_1(f0(A, B, C, D, E, F, H)) :|: TRUE
4.34/2.15	
4.34/2.15	The start-symbols are:[f1_7]
4.34/2.15	
4.34/2.15	
4.34/2.15	----------------------------------------
4.34/2.15	
4.34/2.15	(1) Loat Proof (FINISHED)
4.34/2.15	
4.34/2.15	
4.34/2.15	### Pre-processing the ITS problem ###
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Initial linear ITS problem
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	      0: f0 -> f2 : A'=free_1, C'=free, [ A>=B ], cost: 1
4.34/2.15	
4.34/2.15	      1: f0 -> f0 : A'=free_3, D'=free_2, E'=0, [ B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      2: f0 -> f0 : A'=free_7, D'=free_4, E'=free_5, F'=free_6, [ 0>=1+free_5 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      3: f0 -> f0 : A'=free_11, D'=free_8, E'=free_9, F'=free_10, [ free_9>=1 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      4: f1 -> f0 : G'=free_12, [], cost: 1
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Removed unreachable and leaf rules:
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	      1: f0 -> f0 : A'=free_3, D'=free_2, E'=0, [ B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      2: f0 -> f0 : A'=free_7, D'=free_4, E'=free_5, F'=free_6, [ 0>=1+free_5 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      3: f0 -> f0 : A'=free_11, D'=free_8, E'=free_9, F'=free_10, [ free_9>=1 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      4: f1 -> f0 : G'=free_12, [], cost: 1
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	### Simplification by acceleration and chaining ###
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Accelerating simple loops of location 0.
4.34/2.15	
4.34/2.15	   Accelerating the following rules:
4.34/2.15	
4.34/2.15	      1: f0 -> f0 : A'=free_3, D'=free_2, E'=0, [ B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      2: f0 -> f0 : A'=free_7, D'=free_4, E'=free_5, F'=free_6, [ 0>=1+free_5 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      3: f0 -> f0 : A'=free_11, D'=free_8, E'=free_9, F'=free_10, [ free_9>=1 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	   Accelerated rule 1 with NONTERM (after strengthening guard), yielding the new rule 5.
4.34/2.15	
4.34/2.15	   Accelerated rule 2 with NONTERM (after strengthening guard), yielding the new rule 6.
4.34/2.15	
4.34/2.15	   Accelerated rule 3 with NONTERM (after strengthening guard), yielding the new rule 7.
4.34/2.15	
4.34/2.15	   Removing the simple loops:.
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Accelerated all simple loops using metering functions (where possible):
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	      1: f0 -> f0 : A'=free_3, D'=free_2, E'=0, [ B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      2: f0 -> f0 : A'=free_7, D'=free_4, E'=free_5, F'=free_6, [ 0>=1+free_5 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      3: f0 -> f0 : A'=free_11, D'=free_8, E'=free_9, F'=free_10, [ free_9>=1 && B>=1+A ], cost: 1
4.34/2.15	
4.34/2.15	      5: f0 -> [3] : [ B>=1+A && B>=1+free_3 ], cost: INF
4.34/2.15	
4.34/2.15	      6: f0 -> [3] : [ 0>=1+free_5 && B>=1+A && B>=1+free_7 ], cost: INF
4.34/2.15	
4.34/2.15	      7: f0 -> [3] : [ free_9>=1 && B>=1+A && B>=1+free_11 ], cost: INF
4.34/2.15	
4.34/2.15	      4: f1 -> f0 : G'=free_12, [], cost: 1
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Chained accelerated rules (with incoming rules):
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	      4: f1 -> f0 : G'=free_12, [], cost: 1
4.34/2.15	
4.34/2.15	      8: f1 -> f0 : A'=free_3, D'=free_2, E'=0, G'=free_12, [ B>=1+A ], cost: 2
4.34/2.15	
4.34/2.15	      9: f1 -> f0 : A'=free_7, D'=free_4, E'=free_5, F'=free_6, G'=free_12, [ 0>=1+free_5 && B>=1+A ], cost: 2
4.34/2.15	
4.34/2.15	     10: f1 -> f0 : A'=free_11, D'=free_8, E'=free_9, F'=free_10, G'=free_12, [ free_9>=1 && B>=1+A ], cost: 2
4.34/2.15	
4.34/2.15	     11: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	     12: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	     13: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Removed unreachable locations (and leaf rules with constant cost):
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	     11: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	     12: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	     13: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	### Computing asymptotic complexity ###
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Fully simplified ITS problem
4.34/2.15	
4.34/2.15	   Start location: f1
4.34/2.15	
4.34/2.15	     13: f1 -> [3] : G'=free_12, [ B>=1+A ], cost: INF
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Computing asymptotic complexity for rule 13
4.34/2.15	
4.34/2.15	   Resulting cost INF has complexity: Nonterm
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Found new complexity Nonterm.
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	Obtained the following overall complexity (w.r.t. the length of the input n):
4.34/2.15	
4.34/2.15	   Complexity:  Nonterm
4.34/2.15	
4.34/2.15	   Cpx degree:  Nonterm
4.34/2.15	
4.34/2.15	   Solved cost: INF
4.34/2.15	
4.34/2.15	   Rule cost:   INF
4.34/2.15	
4.34/2.15	   Rule guard:  [ B>=1+A ]
4.34/2.15	
4.34/2.15	
4.34/2.15	
4.34/2.15	NO
4.34/2.15	
4.34/2.15	
4.34/2.15	----------------------------------------
4.34/2.15	
4.34/2.15	(2)
4.34/2.15	BOUNDS(INF, INF)
4.34/2.16	EOF