3.83/2.33	WORST_CASE(NON_POLY, ?)
3.92/2.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.92/2.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/2.33	
3.92/2.33	
3.92/2.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.92/2.33	
3.92/2.33	(0) CpxIntTrs
3.92/2.33	(1) Loat Proof [FINISHED, 146 ms]
3.92/2.33	(2) BOUNDS(INF, INF)
3.92/2.33	
3.92/2.33	
3.92/2.33	----------------------------------------
3.92/2.33	
3.92/2.33	(0)
3.92/2.33	Obligation:
3.92/2.33	Complexity Int TRS consisting of the following rules:
3.92/2.33	f1(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, I, J, K, F, G, H)) :|: A >= B + 1
3.92/2.33	f1(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, I, J, K, F, G, H)) :|: B >= A + 1
3.92/2.33	f1(A, B, C, D, E, F, G, H) -> Com_1(f300(A, A, I, J, E, K, G, H)) :|: A >= B && A <= B
3.92/2.33	f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, I, J)) :|: TRUE
3.92/2.33	
3.92/2.33	The start-symbols are:[f2_8]
3.92/2.33	
3.92/2.33	
3.92/2.33	----------------------------------------
3.92/2.33	
3.92/2.33	(1) Loat Proof (FINISHED)
3.92/2.33	
3.92/2.33	
3.92/2.33	### Pre-processing the ITS problem ###
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Initial linear ITS problem
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      0: f1 -> f1 : C'=free, D'=free_1, E'=free_2, [ A>=1+B ], cost: 1
3.92/2.33	
3.92/2.33	      1: f1 -> f1 : C'=free_3, D'=free_4, E'=free_5, [ B>=1+A ], cost: 1
3.92/2.33	
3.92/2.33	      2: f1 -> f300 : B'=A, C'=free_6, D'=free_7, F'=free_8, [ A==B ], cost: 1
3.92/2.33	
3.92/2.33	      3: f2 -> f1 : G'=free_9, H'=free_10, [], cost: 1
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Removed unreachable and leaf rules:
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      0: f1 -> f1 : C'=free, D'=free_1, E'=free_2, [ A>=1+B ], cost: 1
3.92/2.33	
3.92/2.33	      1: f1 -> f1 : C'=free_3, D'=free_4, E'=free_5, [ B>=1+A ], cost: 1
3.92/2.33	
3.92/2.33	      3: f2 -> f1 : G'=free_9, H'=free_10, [], cost: 1
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	### Simplification by acceleration and chaining ###
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Accelerating simple loops of location 0.
3.92/2.33	
3.92/2.33	   Accelerating the following rules:
3.92/2.33	
3.92/2.33	      0: f1 -> f1 : C'=free, D'=free_1, E'=free_2, [ A>=1+B ], cost: 1
3.92/2.33	
3.92/2.33	      1: f1 -> f1 : C'=free_3, D'=free_4, E'=free_5, [ B>=1+A ], cost: 1
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	   Accelerated rule 0 with NONTERM, yielding the new rule 4.
3.92/2.33	
3.92/2.33	   Accelerated rule 1 with NONTERM, yielding the new rule 5.
3.92/2.33	
3.92/2.33	   Removing the simple loops: 0 1.
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Accelerated all simple loops using metering functions (where possible):
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      4: f1 -> [3] : [ A>=1+B ], cost: INF
3.92/2.33	
3.92/2.33	      5: f1 -> [3] : [ B>=1+A ], cost: INF
3.92/2.33	
3.92/2.33	      3: f2 -> f1 : G'=free_9, H'=free_10, [], cost: 1
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Chained accelerated rules (with incoming rules):
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      3: f2 -> f1 : G'=free_9, H'=free_10, [], cost: 1
3.92/2.33	
3.92/2.33	      6: f2 -> [3] : G'=free_9, H'=free_10, [ A>=1+B ], cost: INF
3.92/2.33	
3.92/2.33	      7: f2 -> [3] : G'=free_9, H'=free_10, [ B>=1+A ], cost: INF
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Removed unreachable locations (and leaf rules with constant cost):
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      6: f2 -> [3] : G'=free_9, H'=free_10, [ A>=1+B ], cost: INF
3.92/2.33	
3.92/2.33	      7: f2 -> [3] : G'=free_9, H'=free_10, [ B>=1+A ], cost: INF
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	### Computing asymptotic complexity ###
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Fully simplified ITS problem
3.92/2.33	
3.92/2.33	   Start location: f2
3.92/2.33	
3.92/2.33	      6: f2 -> [3] : G'=free_9, H'=free_10, [ A>=1+B ], cost: INF
3.92/2.33	
3.92/2.33	      7: f2 -> [3] : G'=free_9, H'=free_10, [ B>=1+A ], cost: INF
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Computing asymptotic complexity for rule 6
3.92/2.33	
3.92/2.33	   Resulting cost INF has complexity: Nonterm
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Found new complexity Nonterm.
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	Obtained the following overall complexity (w.r.t. the length of the input n):
3.92/2.33	
3.92/2.33	   Complexity:  Nonterm
3.92/2.33	
3.92/2.33	   Cpx degree:  Nonterm
3.92/2.33	
3.92/2.33	   Solved cost: INF
3.92/2.33	
3.92/2.33	   Rule cost:   INF
3.92/2.33	
3.92/2.33	   Rule guard:  [ A>=1+B ]
3.92/2.33	
3.92/2.33	
3.92/2.33	
3.92/2.33	NO
3.92/2.33	
3.92/2.33	
3.92/2.33	----------------------------------------
3.92/2.33	
3.92/2.33	(2)
3.92/2.33	BOUNDS(INF, INF)
3.92/2.38	EOF