3.48/1.95	WORST_CASE(NON_POLY, ?)
3.48/1.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.48/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.48/1.96	
3.48/1.96	
3.48/1.96	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.48/1.96	
3.48/1.96	(0) CpxIntTrs
3.48/1.96	(1) Loat Proof [FINISHED, 217 ms]
3.48/1.96	(2) BOUNDS(INF, INF)
3.48/1.96	
3.48/1.96	
3.48/1.96	----------------------------------------
3.48/1.96	
3.48/1.96	(0)
3.48/1.96	Obligation:
3.48/1.96	Complexity Int TRS consisting of the following rules:
3.48/1.96	f2(A, B, C) -> Com_1(f2(1 + A, B, C)) :|: B >= 1 + A
3.48/1.96	f2(A, B, C) -> Com_1(f2(1 + A, B, C)) :|: A >= 1 + B && A >= B
3.48/1.96	f2(A, B, C) -> Com_1(f300(A, B, D)) :|: A >= B && A <= B
3.48/1.96	f1(A, B, C) -> Com_1(f2(A, B, C)) :|: TRUE
3.48/1.96	
3.48/1.96	The start-symbols are:[f1_3]
3.48/1.96	
3.48/1.96	
3.48/1.96	----------------------------------------
3.48/1.96	
3.48/1.96	(1) Loat Proof (FINISHED)
3.48/1.96	
3.48/1.96	
3.48/1.96	### Pre-processing the ITS problem ###
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Initial linear ITS problem
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      0: f2 -> f2 : B'=1+B, [ A>=1+B ], cost: 1
3.48/1.96	
3.48/1.96	      1: f2 -> f2 : B'=1+B, [ B>=1+A && B>=A ], cost: 1
3.48/1.96	
3.48/1.96	      2: f2 -> f300 : C'=free, [ B==A ], cost: 1
3.48/1.96	
3.48/1.96	      3: f1 -> f2 : [], cost: 1
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Removed unreachable and leaf rules:
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      0: f2 -> f2 : B'=1+B, [ A>=1+B ], cost: 1
3.48/1.96	
3.48/1.96	      1: f2 -> f2 : B'=1+B, [ B>=1+A && B>=A ], cost: 1
3.48/1.96	
3.48/1.96	      3: f1 -> f2 : [], cost: 1
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Simplified all rules, resulting in:
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      0: f2 -> f2 : B'=1+B, [ A>=1+B ], cost: 1
3.48/1.96	
3.48/1.96	      1: f2 -> f2 : B'=1+B, [ B>=1+A ], cost: 1
3.48/1.96	
3.48/1.96	      3: f1 -> f2 : [], cost: 1
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	### Simplification by acceleration and chaining ###
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Accelerating simple loops of location 0.
3.48/1.96	
3.48/1.96	   Accelerating the following rules:
3.48/1.96	
3.48/1.96	      0: f2 -> f2 : B'=1+B, [ A>=1+B ], cost: 1
3.48/1.96	
3.48/1.96	      1: f2 -> f2 : B'=1+B, [ B>=1+A ], cost: 1
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	   Accelerated rule 0 with metering function A-B, yielding the new rule 4.
3.48/1.96	
3.48/1.96	   Accelerated rule 1 with NONTERM, yielding the new rule 5.
3.48/1.96	
3.48/1.96	   Removing the simple loops: 0 1.
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Accelerated all simple loops using metering functions (where possible):
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      4: f2 -> f2 : B'=A, [ A>=1+B ], cost: A-B
3.48/1.96	
3.48/1.96	      5: f2 -> [3] : [ B>=1+A ], cost: INF
3.48/1.96	
3.48/1.96	      3: f1 -> f2 : [], cost: 1
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Chained accelerated rules (with incoming rules):
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      3: f1 -> f2 : [], cost: 1
3.48/1.96	
3.48/1.96	      6: f1 -> f2 : B'=A, [ A>=1+B ], cost: 1+A-B
3.48/1.96	
3.48/1.96	      7: f1 -> [3] : [ B>=1+A ], cost: INF
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Removed unreachable locations (and leaf rules with constant cost):
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      6: f1 -> f2 : B'=A, [ A>=1+B ], cost: 1+A-B
3.48/1.96	
3.48/1.96	      7: f1 -> [3] : [ B>=1+A ], cost: INF
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	### Computing asymptotic complexity ###
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Fully simplified ITS problem
3.48/1.96	
3.48/1.96	   Start location: f1
3.48/1.96	
3.48/1.96	      6: f1 -> f2 : B'=A, [ A>=1+B ], cost: 1+A-B
3.48/1.96	
3.48/1.96	      7: f1 -> [3] : [ B>=1+A ], cost: INF
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Computing asymptotic complexity for rule 6
3.48/1.96	
3.48/1.96	   Solved the limit problem by the following transformations:
3.48/1.96	
3.48/1.96	      Created initial limit problem:
3.48/1.96	
3.48/1.96	      1+A-B (+), A-B (+/+!) [not solved]
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	      removing all constraints (solved by SMT)
3.48/1.96	
3.48/1.96	      resulting limit problem: [solved]
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	      applying transformation rule (C) using substitution {A==0,B==-n}
3.48/1.96	
3.48/1.96	      resulting limit problem:
3.48/1.96	
3.48/1.96	      [solved]
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	   Solution:
3.48/1.96	
3.48/1.96	      A / 0
3.48/1.96	
3.48/1.96	      B / -n
3.48/1.96	
3.48/1.96	   Resulting cost 1+n has complexity: Poly(n^1)
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Found new complexity Poly(n^1).
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Computing asymptotic complexity for rule 7
3.48/1.96	
3.48/1.96	   Resulting cost INF has complexity: Nonterm
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Found new complexity Nonterm.
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	Obtained the following overall complexity (w.r.t. the length of the input n):
3.48/1.96	
3.48/1.96	   Complexity:  Nonterm
3.48/1.96	
3.48/1.96	   Cpx degree:  Nonterm
3.48/1.96	
3.48/1.96	   Solved cost: INF
3.48/1.96	
3.48/1.96	   Rule cost:   INF
3.48/1.96	
3.48/1.96	   Rule guard:  [ B>=1+A ]
3.48/1.96	
3.48/1.96	
3.48/1.96	
3.48/1.96	NO
3.48/1.96	
3.48/1.96	
3.48/1.96	----------------------------------------
3.48/1.96	
3.48/1.96	(2)
3.48/1.96	BOUNDS(INF, INF)
4.03/1.99	EOF