9.27/3.99	WORST_CASE(NON_POLY, ?)
9.27/4.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
9.27/4.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.27/4.00	
9.27/4.00	
9.27/4.00	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
9.27/4.00	
9.27/4.00	(0) CpxIntTrs
9.27/4.00	(1) Loat Proof [FINISHED, 2342 ms]
9.27/4.00	(2) BOUNDS(INF, INF)
9.27/4.00	
9.27/4.00	
9.27/4.00	----------------------------------------
9.27/4.00	
9.27/4.00	(0)
9.27/4.00	Obligation:
9.27/4.00	Complexity Int TRS consisting of the following rules:
9.27/4.00	f0(A, B, C, D, E) -> Com_1(f1(F, 1, 0, D, E)) :|: TRUE
9.27/4.00	f1(A, B, C, D, E) -> Com_1(f1(A - 10, B - 1, C, D, E)) :|: B >= 1 && A >= 101
9.27/4.00	f1(A, B, C, D, E) -> Com_1(f1(A + 11, B + 1, C, D, E)) :|: B >= 1 && 100 >= A
9.27/4.00	f1(A, B, C, D, E) -> Com_1(f1(A - 10, B - 1, 1, A, B)) :|: A >= 101 && 0 >= C && B >= 1
9.27/4.00	f1(A, B, C, D, E) -> Com_1(f1(A + 11, B + 1, 1, A, B)) :|: 100 >= A && 0 >= C && B >= 1
9.27/4.00	f1(A, B, C, D, E) -> Com_1(f2(A, B, C, D, E)) :|: D >= A && C >= 1 && B >= E
9.27/4.00	
9.27/4.00	The start-symbols are:[f0_5]
9.27/4.00	
9.27/4.00	
9.27/4.00	----------------------------------------
9.27/4.00	
9.27/4.00	(1) Loat Proof (FINISHED)
9.27/4.00	
9.27/4.00	
9.27/4.00	### Pre-processing the ITS problem ###
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Initial linear ITS problem
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	      0: f0 -> f1 : A'=free, B'=1, C'=0, [], cost: 1
9.27/4.00	
9.27/4.00	      1: f1 -> f1 : A'=-10+A, B'=-1+B, [ B>=1 && A>=101 ], cost: 1
9.27/4.00	
9.27/4.00	      2: f1 -> f1 : A'=11+A, B'=1+B, [ B>=1 && 100>=A ], cost: 1
9.27/4.00	
9.27/4.00	      3: f1 -> f1 : A'=-10+A, B'=-1+B, C'=1, D'=A, E'=B, [ A>=101 && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	      4: f1 -> f1 : A'=11+A, B'=1+B, C'=1, D'=A, E'=B, [ 100>=A && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	      5: f1 -> f2 : [ D>=A && C>=1 && B>=E ], cost: 1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Removed unreachable and leaf rules:
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	      0: f0 -> f1 : A'=free, B'=1, C'=0, [], cost: 1
9.27/4.00	
9.27/4.00	      1: f1 -> f1 : A'=-10+A, B'=-1+B, [ B>=1 && A>=101 ], cost: 1
9.27/4.00	
9.27/4.00	      2: f1 -> f1 : A'=11+A, B'=1+B, [ B>=1 && 100>=A ], cost: 1
9.27/4.00	
9.27/4.00	      3: f1 -> f1 : A'=-10+A, B'=-1+B, C'=1, D'=A, E'=B, [ A>=101 && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	      4: f1 -> f1 : A'=11+A, B'=1+B, C'=1, D'=A, E'=B, [ 100>=A && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	### Simplification by acceleration and chaining ###
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Accelerating simple loops of location 1.
9.27/4.00	
9.27/4.00	   Accelerating the following rules:
9.27/4.00	
9.27/4.00	      1: f1 -> f1 : A'=-10+A, B'=-1+B, [ B>=1 && A>=101 ], cost: 1
9.27/4.00	
9.27/4.00	      2: f1 -> f1 : A'=11+A, B'=1+B, [ B>=1 && 100>=A ], cost: 1
9.27/4.00	
9.27/4.00	      3: f1 -> f1 : A'=-10+A, B'=-1+B, C'=1, D'=A, E'=B, [ A>=101 && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	      4: f1 -> f1 : A'=11+A, B'=1+B, C'=1, D'=A, E'=B, [ 100>=A && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	   Accelerated rule 1 with metering function meter (where 10*meter==-100+A) (after adding A<=B), yielding the new rule 6.
9.27/4.00	
9.27/4.00	   Accelerated rule 1 with backward acceleration, yielding the new rule 7.
9.27/4.00	
9.27/4.00	   Accelerated rule 2 with metering function meter_1 (where 11*meter_1==100-A), yielding the new rule 8.
9.27/4.00	
9.27/4.00	   Found no metering function for rule 3.
9.27/4.00	
9.27/4.00	   Found no metering function for rule 4.
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {meter==1}
9.27/4.00	
9.27/4.00	   Nested simple loops 2 (outer loop) and 6 (inner loop) with metering function 89+10*meter-A, resulting in the new rules: 9.
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {meter==1}
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {meter==1}
9.27/4.00	
9.27/4.00	   Nested simple loops 4 (outer loop) and 6 (inner loop) with metering function 89+10*meter-A, resulting in the new rules: 10.
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {k==-1+B}
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {k==1}
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {meter_1==1}
9.27/4.00	
9.27/4.00	      During metering: Instantiating temporary variables by {meter_1==1}
9.27/4.00	
9.27/4.00	   Removing the simple loops: 1 2 4.
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Accelerated all simple loops using metering functions (where possible):
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	      0: f0 -> f1 : A'=free, B'=1, C'=0, [], cost: 1
9.27/4.00	
9.27/4.00	      3: f1 -> f1 : A'=-10+A, B'=-1+B, C'=1, D'=A, E'=B, [ A>=101 && 0>=C && B>=1 ], cost: 1
9.27/4.00	
9.27/4.00	      6: f1 -> f1 : A'=-10*meter+A, B'=-meter+B, [ B>=1 && A>=101 && A<=B && 10*meter==-100+A && meter>=1 ], cost: meter
9.27/4.00	
9.27/4.00	      7: f1 -> f1 : A'=A-10*k, B'=-k+B, [ B>=1 && A>=101 && k>0 && 1-k+B>=1 && 10+A-10*k>=101 ], cost: k
9.27/4.00	
9.27/4.00	      8: f1 -> f1 : A'=11*meter_1+A, B'=meter_1+B, [ B>=1 && 100>=A && 11*meter_1==100-A && meter_1>=1 ], cost: meter_1
9.27/4.00	
9.27/4.00	      9: f1 -> f1 : A'=979-10*(89+10*meter-A)*meter+110*meter-10*A, B'=89-(89+10*meter-A)*meter+10*meter-A+B, [ B>=1 && 100>=A && 11+A>=101 && 11+A<=1+B && 10*meter==-89+A && meter>=1 && 89+10*meter-A>=1 ], cost: 89+(89+10*meter-A)*meter+10*meter-A
9.27/4.00	
9.27/4.00	     10: f1 -> f1 : A'=979-10*(89+10*meter-A)*meter+110*meter-10*A, B'=89-(89+10*meter-A)*meter+10*meter-A+B, C'=1, D'=968-10*(89+10*meter-A)*meter+120*meter-10*A, E'=88-(89+10*meter-A)*meter+11*meter-A+B, [ 100>=A && 0>=C && B>=1 && 11+A>=101 && 11+A<=1+B && 10*meter==-89+A && meter>=1 && 89+10*meter-A>=1 ], cost: 89+(89+10*meter-A)*meter+10*meter-A
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Chained accelerated rules (with incoming rules):
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	      0: f0 -> f1 : A'=free, B'=1, C'=0, [], cost: 1
9.27/4.00	
9.27/4.00	     11: f0 -> f1 : A'=-10+free, B'=0, C'=1, D'=free, E'=1, [ free>=101 ], cost: 2
9.27/4.00	
9.27/4.00	     12: f0 -> f1 : A'=-10+free, B'=0, C'=0, [ free>=101 ], cost: 2
9.27/4.00	
9.27/4.00	     13: f0 -> f1 : A'=100, B'=1+meter_1, C'=0, [ 100>=100-11*meter_1 && meter_1>=1 ], cost: 1+meter_1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Removed unreachable locations (and leaf rules with constant cost):
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	     13: f0 -> f1 : A'=100, B'=1+meter_1, C'=0, [ 100>=100-11*meter_1 && meter_1>=1 ], cost: 1+meter_1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	### Computing asymptotic complexity ###
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Fully simplified ITS problem
9.27/4.00	
9.27/4.00	   Start location: f0
9.27/4.00	
9.27/4.00	     13: f0 -> f1 : A'=100, B'=1+meter_1, C'=0, [ 100>=100-11*meter_1 && meter_1>=1 ], cost: 1+meter_1
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Computing asymptotic complexity for rule 13
9.27/4.00	
9.27/4.00	   Simplified the guard:
9.27/4.00	
9.27/4.00	     13: f0 -> f1 : A'=100, B'=1+meter_1, C'=0, [ meter_1>=1 ], cost: 1+meter_1
9.27/4.00	
9.27/4.00	   Solved the limit problem by the following transformations:
9.27/4.00	
9.27/4.00	      Created initial limit problem:
9.27/4.00	
9.27/4.00	      1+meter_1 (+), meter_1 (+/+!) [not solved]
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	      removing all constraints (solved by SMT)
9.27/4.00	
9.27/4.00	      resulting limit problem: [solved]
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	      applying transformation rule (C) using substitution {meter_1==n}
9.27/4.00	
9.27/4.00	      resulting limit problem:
9.27/4.00	
9.27/4.00	      [solved]
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	   Solution:
9.27/4.00	
9.27/4.00	      meter_1 / n
9.27/4.00	
9.27/4.00	   Resulting cost 1+n has complexity: Unbounded
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Found new complexity Unbounded.
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	Obtained the following overall complexity (w.r.t. the length of the input n):
9.27/4.00	
9.27/4.00	   Complexity:  Unbounded
9.27/4.00	
9.27/4.00	   Cpx degree:  Unbounded
9.27/4.00	
9.27/4.00	   Solved cost: 1+n
9.27/4.00	
9.27/4.00	   Rule cost:   1+meter_1
9.27/4.00	
9.27/4.00	   Rule guard:  [ meter_1>=1 ]
9.27/4.00	
9.27/4.00	
9.27/4.00	
9.27/4.00	WORST_CASE(INF,?)
9.27/4.00	
9.27/4.00	
9.27/4.00	----------------------------------------
9.27/4.00	
9.27/4.00	(2)
9.27/4.00	BOUNDS(INF, INF)
9.40/4.02	EOF