3.86/1.88	WORST_CASE(NON_POLY, ?)
3.86/1.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.86/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.86/1.89	
3.86/1.89	
3.86/1.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.86/1.89	
3.86/1.89	(0) CpxIntTrs
3.86/1.89	(1) Loat Proof [FINISHED, 222 ms]
3.86/1.89	(2) BOUNDS(INF, INF)
3.86/1.89	
3.86/1.89	
3.86/1.89	----------------------------------------
3.86/1.89	
3.86/1.89	(0)
3.86/1.89	Obligation:
3.86/1.89	Complexity Int TRS consisting of the following rules:
3.86/1.89	f1(A, B) -> Com_1(f0(A, B)) :|: TRUE
3.86/1.89	f0(A, B) -> Com_1(f0(A + B, B)) :|: A >= 1 && B >= 1
3.86/1.89	f0(A, B) -> Com_1(f0(A + B, B)) :|: A >= 1 && 0 >= B + 1
3.86/1.89	
3.86/1.89	The start-symbols are:[f1_2]
3.86/1.89	
3.86/1.89	
3.86/1.89	----------------------------------------
3.86/1.89	
3.86/1.89	(1) Loat Proof (FINISHED)
3.86/1.89	
3.86/1.89	
3.86/1.89	### Pre-processing the ITS problem ###
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Initial linear ITS problem
3.86/1.89	
3.86/1.89	   Start location: f1
3.86/1.89	
3.86/1.89	      0: f1 -> f0 : [], cost: 1
3.86/1.89	
3.86/1.89	      1: f0 -> f0 : A'=A+B, [ A>=1 && B>=1 ], cost: 1
3.86/1.89	
3.86/1.89	      2: f0 -> f0 : A'=A+B, [ A>=1 && 0>=1+B ], cost: 1
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	### Simplification by acceleration and chaining ###
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Accelerating simple loops of location 1.
3.86/1.89	
3.86/1.89	   Accelerating the following rules:
3.86/1.89	
3.86/1.89	      1: f0 -> f0 : A'=A+B, [ A>=1 && B>=1 ], cost: 1
3.86/1.89	
3.86/1.89	      2: f0 -> f0 : A'=A+B, [ A>=1 && 0>=1+B ], cost: 1
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	   Accelerated rule 1 with NONTERM, yielding the new rule 3.
3.86/1.89	
3.86/1.89	   Accelerated rule 2 with backward acceleration, yielding the new rule 4.
3.86/1.89	
3.86/1.89	   Removing the simple loops: 1 2.
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Accelerated all simple loops using metering functions (where possible):
3.86/1.89	
3.86/1.89	   Start location: f1
3.86/1.89	
3.86/1.89	      0: f1 -> f0 : [], cost: 1
3.86/1.89	
3.86/1.89	      3: f0 -> [2] : [ A>=1 && B>=1 ], cost: INF
3.86/1.89	
3.86/1.89	      4: f0 -> f0 : A'=k*B+A, [ A>=1 && 0>=1+B && k>0 && (-1+k)*B+A>=1 ], cost: k
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Chained accelerated rules (with incoming rules):
3.86/1.89	
3.86/1.89	   Start location: f1
3.86/1.89	
3.86/1.89	      0: f1 -> f0 : [], cost: 1
3.86/1.89	
3.86/1.89	      5: f1 -> [2] : [ A>=1 && B>=1 ], cost: INF
3.86/1.89	
3.86/1.89	      6: f1 -> f0 : A'=k*B+A, [ A>=1 && 0>=1+B && k>0 && (-1+k)*B+A>=1 ], cost: 1+k
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Removed unreachable locations (and leaf rules with constant cost):
3.86/1.89	
3.86/1.89	   Start location: f1
3.86/1.89	
3.86/1.89	      5: f1 -> [2] : [ A>=1 && B>=1 ], cost: INF
3.86/1.89	
3.86/1.89	      6: f1 -> f0 : A'=k*B+A, [ A>=1 && 0>=1+B && k>0 && (-1+k)*B+A>=1 ], cost: 1+k
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	### Computing asymptotic complexity ###
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Fully simplified ITS problem
3.86/1.89	
3.86/1.89	   Start location: f1
3.86/1.89	
3.86/1.89	      5: f1 -> [2] : [ A>=1 && B>=1 ], cost: INF
3.86/1.89	
3.86/1.89	      6: f1 -> f0 : A'=k*B+A, [ A>=1 && 0>=1+B && k>0 && (-1+k)*B+A>=1 ], cost: 1+k
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Computing asymptotic complexity for rule 5
3.86/1.89	
3.86/1.89	   Resulting cost INF has complexity: Nonterm
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Found new complexity Nonterm.
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	Obtained the following overall complexity (w.r.t. the length of the input n):
3.86/1.89	
3.86/1.89	   Complexity:  Nonterm
3.86/1.89	
3.86/1.89	   Cpx degree:  Nonterm
3.86/1.89	
3.86/1.89	   Solved cost: INF
3.86/1.89	
3.86/1.89	   Rule cost:   INF
3.86/1.89	
3.86/1.89	   Rule guard:  [ A>=1 && B>=1 ]
3.86/1.89	
3.86/1.89	
3.86/1.89	
3.86/1.89	NO
3.86/1.89	
3.86/1.89	
3.86/1.89	----------------------------------------
3.86/1.89	
3.86/1.89	(2)
3.86/1.89	BOUNDS(INF, INF)
3.86/1.91	EOF