4.08/2.05	WORST_CASE(NON_POLY, ?)
4.08/2.06	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.08/2.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.08/2.06	
4.08/2.06	
4.08/2.06	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.08/2.06	
4.08/2.06	(0) CpxIntTrs
4.08/2.06	(1) Loat Proof [FINISHED, 417 ms]
4.08/2.06	(2) BOUNDS(INF, INF)
4.08/2.06	
4.08/2.06	
4.08/2.06	----------------------------------------
4.08/2.06	
4.08/2.06	(0)
4.08/2.06	Obligation:
4.08/2.06	Complexity Int TRS consisting of the following rules:
4.08/2.06	f7(A, B) -> Com_1(f7(C, B)) :|: 0 >= A + 1
4.08/2.06	f7(A, B) -> Com_1(f7(C, B)) :|: A >= 1
4.08/2.06	f13(A, B) -> Com_1(f13(A, B)) :|: TRUE
4.08/2.06	f15(A, B) -> Com_1(f17(A, B)) :|: TRUE
4.08/2.06	f7(A, B) -> Com_1(f13(0, 1)) :|: A >= 0 && A <= 0
4.08/2.06	f0(A, B) -> Com_1(f7(C, 1)) :|: TRUE
4.08/2.06	
4.08/2.06	The start-symbols are:[f0_2]
4.08/2.06	
4.08/2.06	
4.08/2.06	----------------------------------------
4.08/2.06	
4.08/2.06	(1) Loat Proof (FINISHED)
4.08/2.06	
4.08/2.06	
4.08/2.06	### Pre-processing the ITS problem ###
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Initial linear ITS problem
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	      0: f7 -> f7 : A'=free, [ 0>=1+A ], cost: 1
4.08/2.06	
4.08/2.06	      1: f7 -> f7 : A'=free_1, [ A>=1 ], cost: 1
4.08/2.06	
4.08/2.06	      4: f7 -> f13 : A'=0, B'=1, [ A==0 ], cost: 1
4.08/2.06	
4.08/2.06	      2: f13 -> f13 : [], cost: 1
4.08/2.06	
4.08/2.06	      3: f15 -> f17 : [], cost: 1
4.08/2.06	
4.08/2.06	      5: f0 -> f7 : A'=free_2, B'=1, [], cost: 1
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Removed unreachable and leaf rules:
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	      0: f7 -> f7 : A'=free, [ 0>=1+A ], cost: 1
4.08/2.06	
4.08/2.06	      1: f7 -> f7 : A'=free_1, [ A>=1 ], cost: 1
4.08/2.06	
4.08/2.06	      4: f7 -> f13 : A'=0, B'=1, [ A==0 ], cost: 1
4.08/2.06	
4.08/2.06	      2: f13 -> f13 : [], cost: 1
4.08/2.06	
4.08/2.06	      5: f0 -> f7 : A'=free_2, B'=1, [], cost: 1
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	### Simplification by acceleration and chaining ###
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Accelerating simple loops of location 0.
4.08/2.06	
4.08/2.06	   Accelerating the following rules:
4.08/2.06	
4.08/2.06	      0: f7 -> f7 : A'=free, [ 0>=1+A ], cost: 1
4.08/2.06	
4.08/2.06	      1: f7 -> f7 : A'=free_1, [ A>=1 ], cost: 1
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	   Accelerated rule 0 with NONTERM (after strengthening guard), yielding the new rule 6.
4.08/2.06	
4.08/2.06	   Accelerated rule 1 with NONTERM (after strengthening guard), yielding the new rule 7.
4.08/2.06	
4.08/2.06	   Removing the simple loops:.
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Accelerating simple loops of location 1.
4.08/2.06	
4.08/2.06	   Accelerating the following rules:
4.08/2.06	
4.08/2.06	      2: f13 -> f13 : [], cost: 1
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.08/2.06	
4.08/2.06	   Removing the simple loops: 2.
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Accelerated all simple loops using metering functions (where possible):
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	      0: f7 -> f7 : A'=free, [ 0>=1+A ], cost: 1
4.08/2.06	
4.08/2.06	      1: f7 -> f7 : A'=free_1, [ A>=1 ], cost: 1
4.08/2.06	
4.08/2.06	      4: f7 -> f13 : A'=0, B'=1, [ A==0 ], cost: 1
4.08/2.06	
4.08/2.06	      6: f7 -> [5] : [ 0>=1+A && 0>=1+free ], cost: INF
4.08/2.06	
4.08/2.06	      7: f7 -> [5] : [ A>=1 && free_1>=1 ], cost: INF
4.08/2.06	
4.08/2.06	      8: f13 -> [6] : [], cost: INF
4.08/2.06	
4.08/2.06	      5: f0 -> f7 : A'=free_2, B'=1, [], cost: 1
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Chained accelerated rules (with incoming rules):
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	      4: f7 -> f13 : A'=0, B'=1, [ A==0 ], cost: 1
4.08/2.06	
4.08/2.06	     13: f7 -> [6] : A'=0, B'=1, [ A==0 ], cost: INF
4.08/2.06	
4.08/2.06	      5: f0 -> f7 : A'=free_2, B'=1, [], cost: 1
4.08/2.06	
4.08/2.06	      9: f0 -> f7 : A'=free, B'=1, [], cost: 2
4.08/2.06	
4.08/2.06	     10: f0 -> f7 : A'=free_1, B'=1, [], cost: 2
4.08/2.06	
4.08/2.06	     11: f0 -> [5] : A'=free_2, B'=1, [ 0>=1+free_2 ], cost: INF
4.08/2.06	
4.08/2.06	     12: f0 -> [5] : A'=free_2, B'=1, [ free_2>=1 ], cost: INF
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Removed unreachable locations (and leaf rules with constant cost):
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	     13: f7 -> [6] : A'=0, B'=1, [ A==0 ], cost: INF
4.08/2.06	
4.08/2.06	      5: f0 -> f7 : A'=free_2, B'=1, [], cost: 1
4.08/2.06	
4.08/2.06	      9: f0 -> f7 : A'=free, B'=1, [], cost: 2
4.08/2.06	
4.08/2.06	     10: f0 -> f7 : A'=free_1, B'=1, [], cost: 2
4.08/2.06	
4.08/2.06	     11: f0 -> [5] : A'=free_2, B'=1, [ 0>=1+free_2 ], cost: INF
4.08/2.06	
4.08/2.06	     12: f0 -> [5] : A'=free_2, B'=1, [ free_2>=1 ], cost: INF
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Eliminated locations (on tree-shaped paths):
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	     11: f0 -> [5] : A'=free_2, B'=1, [ 0>=1+free_2 ], cost: INF
4.08/2.06	
4.08/2.06	     12: f0 -> [5] : A'=free_2, B'=1, [ free_2>=1 ], cost: INF
4.08/2.06	
4.08/2.06	     14: f0 -> [6] : A'=0, B'=1, [ free_2==0 ], cost: INF
4.08/2.06	
4.08/2.06	     15: f0 -> [6] : A'=0, B'=1, [ free==0 ], cost: INF
4.08/2.06	
4.08/2.06	     16: f0 -> [6] : A'=0, B'=1, [ free_1==0 ], cost: INF
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	### Computing asymptotic complexity ###
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Fully simplified ITS problem
4.08/2.06	
4.08/2.06	   Start location: f0
4.08/2.06	
4.08/2.06	     11: f0 -> [5] : A'=free_2, B'=1, [ 0>=1+free_2 ], cost: INF
4.08/2.06	
4.08/2.06	     12: f0 -> [5] : A'=free_2, B'=1, [ free_2>=1 ], cost: INF
4.08/2.06	
4.08/2.06	     14: f0 -> [6] : A'=0, B'=1, [ free_2==0 ], cost: INF
4.08/2.06	
4.08/2.06	     15: f0 -> [6] : A'=0, B'=1, [ free==0 ], cost: INF
4.08/2.06	
4.08/2.06	     16: f0 -> [6] : A'=0, B'=1, [ free_1==0 ], cost: INF
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Computing asymptotic complexity for rule 11
4.08/2.06	
4.08/2.06	   Resulting cost INF has complexity: Nonterm
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Found new complexity Nonterm.
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	Obtained the following overall complexity (w.r.t. the length of the input n):
4.08/2.06	
4.08/2.06	   Complexity:  Nonterm
4.08/2.06	
4.08/2.06	   Cpx degree:  Nonterm
4.08/2.06	
4.08/2.06	   Solved cost: INF
4.08/2.06	
4.08/2.06	   Rule cost:   INF
4.08/2.06	
4.08/2.06	   Rule guard:  [ 0>=1+free_2 ]
4.08/2.06	
4.08/2.06	
4.08/2.06	
4.08/2.06	NO
4.08/2.06	
4.08/2.06	
4.08/2.06	----------------------------------------
4.08/2.06	
4.08/2.06	(2)
4.08/2.06	BOUNDS(INF, INF)
4.19/2.07	EOF