4.43/2.27	WORST_CASE(NON_POLY, ?)
4.43/2.28	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.43/2.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.43/2.28	
4.43/2.28	
4.43/2.28	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.43/2.28	
4.43/2.28	(0) CpxIntTrs
4.43/2.28	(1) Loat Proof [FINISHED, 407 ms]
4.43/2.28	(2) BOUNDS(INF, INF)
4.43/2.28	
4.43/2.28	
4.43/2.28	----------------------------------------
4.43/2.28	
4.43/2.28	(0)
4.43/2.28	Obligation:
4.43/2.28	Complexity Int TRS consisting of the following rules:
4.43/2.28	f2(A, B, C) -> Com_1(f2(-(1) + A, D, C)) :|: D >= 1 && A >= 2
4.43/2.28	f2(A, B, C) -> Com_1(f2(-(1) + A, D, C)) :|: 0 >= D + 1 && A >= 2
4.43/2.28	f2(A, B, C) -> Com_1(f1(-(1) + A, D, E)) :|: D >= 1 && 1 >= A
4.43/2.28	f2(A, B, C) -> Com_1(f1(-(1) + A, D, E)) :|: 0 >= D + 1 && 1 >= A
4.43/2.28	f2(A, B, C) -> Com_1(f2(A, 0, C)) :|: A >= 1
4.43/2.28	f2(A, B, C) -> Com_1(f1(A, 0, D)) :|: 0 >= A
4.43/2.28	f300(A, B, C) -> Com_1(f2(A, B, C)) :|: TRUE
4.43/2.28	
4.43/2.28	The start-symbols are:[f300_3]
4.43/2.28	
4.43/2.28	
4.43/2.28	----------------------------------------
4.43/2.28	
4.43/2.28	(1) Loat Proof (FINISHED)
4.43/2.28	
4.43/2.28	
4.43/2.28	### Pre-processing the ITS problem ###
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Initial linear ITS problem
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	      0: f2 -> f2 : A'=-1+A, B'=free, [ free>=1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      1: f2 -> f2 : A'=-1+A, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      2: f2 -> f1 : A'=-1+A, B'=free_2, C'=free_3, [ free_2>=1 && 1>=A ], cost: 1
4.43/2.28	
4.43/2.28	      3: f2 -> f1 : A'=-1+A, B'=free_4, C'=free_5, [ 0>=1+free_4 && 1>=A ], cost: 1
4.43/2.28	
4.43/2.28	      4: f2 -> f2 : B'=0, [ A>=1 ], cost: 1
4.43/2.28	
4.43/2.28	      5: f2 -> f1 : B'=0, C'=free_6, [ 0>=A ], cost: 1
4.43/2.28	
4.43/2.28	      6: f300 -> f2 : [], cost: 1
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Removed unreachable and leaf rules:
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	      0: f2 -> f2 : A'=-1+A, B'=free, [ free>=1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      1: f2 -> f2 : A'=-1+A, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      4: f2 -> f2 : B'=0, [ A>=1 ], cost: 1
4.43/2.28	
4.43/2.28	      6: f300 -> f2 : [], cost: 1
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	### Simplification by acceleration and chaining ###
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Accelerating simple loops of location 0.
4.43/2.28	
4.43/2.28	   Accelerating the following rules:
4.43/2.28	
4.43/2.28	      0: f2 -> f2 : A'=-1+A, B'=free, [ free>=1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      1: f2 -> f2 : A'=-1+A, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: 1
4.43/2.28	
4.43/2.28	      4: f2 -> f2 : B'=0, [ A>=1 ], cost: 1
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	   Accelerated rule 0 with metering function -1+A, yielding the new rule 7.
4.43/2.28	
4.43/2.28	   Accelerated rule 1 with metering function -1+A, yielding the new rule 8.
4.43/2.28	
4.43/2.28	   Accelerated rule 4 with NONTERM, yielding the new rule 9.
4.43/2.28	
4.43/2.28	   Removing the simple loops: 0 1 4.
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Accelerated all simple loops using metering functions (where possible):
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	      7: f2 -> f2 : A'=1, B'=free, [ free>=1 && A>=2 ], cost: -1+A
4.43/2.28	
4.43/2.28	      8: f2 -> f2 : A'=1, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: -1+A
4.43/2.28	
4.43/2.28	      9: f2 -> [3] : [ A>=1 ], cost: INF
4.43/2.28	
4.43/2.28	      6: f300 -> f2 : [], cost: 1
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Chained accelerated rules (with incoming rules):
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	      6: f300 -> f2 : [], cost: 1
4.43/2.28	
4.43/2.28	     10: f300 -> f2 : A'=1, B'=free, [ free>=1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     11: f300 -> f2 : A'=1, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     12: f300 -> [3] : [ A>=1 ], cost: INF
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Removed unreachable locations (and leaf rules with constant cost):
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	     10: f300 -> f2 : A'=1, B'=free, [ free>=1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     11: f300 -> f2 : A'=1, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     12: f300 -> [3] : [ A>=1 ], cost: INF
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	### Computing asymptotic complexity ###
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Fully simplified ITS problem
4.43/2.28	
4.43/2.28	   Start location: f300
4.43/2.28	
4.43/2.28	     10: f300 -> f2 : A'=1, B'=free, [ free>=1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     11: f300 -> f2 : A'=1, B'=free_1, [ 0>=1+free_1 && A>=2 ], cost: A
4.43/2.28	
4.43/2.28	     12: f300 -> [3] : [ A>=1 ], cost: INF
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Computing asymptotic complexity for rule 10
4.43/2.28	
4.43/2.28	   Solved the limit problem by the following transformations:
4.43/2.28	
4.43/2.28	      Created initial limit problem:
4.43/2.28	
4.43/2.28	      free (+/+!), -1+A (+/+!), A (+) [not solved]
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	      removing all constraints (solved by SMT)
4.43/2.28	
4.43/2.28	      resulting limit problem: [solved]
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	      applying transformation rule (C) using substitution {free==1,A==n}
4.43/2.28	
4.43/2.28	      resulting limit problem:
4.43/2.28	
4.43/2.28	      [solved]
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	   Solution:
4.43/2.28	
4.43/2.28	      free / 1
4.43/2.28	
4.43/2.28	      A / n
4.43/2.28	
4.43/2.28	   Resulting cost n has complexity: Poly(n^1)
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Found new complexity Poly(n^1).
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Computing asymptotic complexity for rule 12
4.43/2.28	
4.43/2.28	   Resulting cost INF has complexity: Nonterm
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Found new complexity Nonterm.
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	Obtained the following overall complexity (w.r.t. the length of the input n):
4.43/2.28	
4.43/2.28	   Complexity:  Nonterm
4.43/2.28	
4.43/2.28	   Cpx degree:  Nonterm
4.43/2.28	
4.43/2.28	   Solved cost: INF
4.43/2.28	
4.43/2.28	   Rule cost:   INF
4.43/2.28	
4.43/2.28	   Rule guard:  [ A>=1 ]
4.43/2.28	
4.43/2.28	
4.43/2.28	
4.43/2.28	NO
4.43/2.28	
4.43/2.28	
4.43/2.28	----------------------------------------
4.43/2.28	
4.43/2.28	(2)
4.43/2.28	BOUNDS(INF, INF)
4.63/2.30	EOF