11.33/8.39	MAYBE
11.33/8.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
11.33/8.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.33/8.40	
11.33/8.40	
11.33/8.40	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
11.33/8.40	
11.33/8.40	(0) CpxIntTrs
11.33/8.40	(1) Loat Proof [FINISHED, 487 ms]
11.33/8.40	(2) BOUNDS(1, INF)
11.33/8.40	
11.33/8.40	
11.33/8.40	----------------------------------------
11.33/8.40	
11.33/8.40	(0)
11.33/8.40	Obligation:
11.33/8.40	Complexity Int TRS consisting of the following rules:
11.33/8.40	eval(A, B) -> Com_1(eval(D, B)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C + 1 && A + B >= 2 * E && 3 * E >= A + B + 1 && E + 1 >= D
11.33/8.40	eval(A, B) -> Com_1(eval(A, D)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C && A + B >= 2 * E && 3 * E >= A + B + 1 && E >= D
11.33/8.40	start(A, B) -> Com_1(eval(A, B)) :|: TRUE
11.33/8.40	
11.33/8.40	The start-symbols are:[start_2]
11.33/8.40	
11.33/8.40	
11.33/8.40	----------------------------------------
11.33/8.40	
11.33/8.40	(1) Loat Proof (FINISHED)
11.33/8.40	
11.33/8.40	
11.33/8.40	### Pre-processing the ITS problem ###
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Initial linear ITS problem
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free_3 && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Simplified all rules, resulting in:
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	### Simplification by acceleration and chaining ###
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Accelerating simple loops of location 0.
11.33/8.40	
11.33/8.40	   Accelerating the following rules:
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	      During metering: Instantiating temporary variables by {free==-1+free_1,free_1==1+free_2,free_2==-1+free_1}
11.33/8.40	
11.33/8.40	   Accelerated rule 0 with metering function -1+free_1-free_2, yielding the new rule 3.
11.33/8.40	
11.33/8.40	      During metering: Instantiating temporary variables by {free_3==free_4,free_4==free_3,free_5==free_4}
11.33/8.40	
11.33/8.40	   Accelerated rule 1 with metering function free_3-free_4, yielding the new rule 4.
11.33/8.40	
11.33/8.40	   Removing the simple loops: 0 1.
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Accelerated all simple loops using metering functions (where possible):
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      3: eval -> eval : A'=1+free_2, [ A>=0 && B>=1+A && -3+3*free_1>=1+A+B && 1+free_2>=free_1 && A+B>=-2+2*free_1 && -1+free_1-free_2>=1 ], cost: -1+free_1-free_2
11.33/8.40	
11.33/8.40	      4: eval -> eval : B'=free_3, [ A>=0 && B>=1+A && 3*free_4>=1+A+B && A+B>=2*free_4 && free_4>=free_3 && free_3-free_4>=1 ], cost: free_3-free_4
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Chained accelerated rules (with incoming rules):
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Removed unreachable locations (and leaf rules with constant cost):
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	### Computing asymptotic complexity ###
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Fully simplified ITS problem
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Obtained the following overall complexity (w.r.t. the length of the input n):
11.33/8.40	
11.33/8.40	   Complexity:  Unknown
11.33/8.40	
11.33/8.40	   Cpx degree:  ?
11.33/8.40	
11.33/8.40	   Solved cost: 0
11.33/8.40	
11.33/8.40	   Rule cost:   0
11.33/8.40	
11.33/8.40	   Rule guard:  []
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	WORST_CASE(Omega(0),?)
11.33/8.40	
11.33/8.40	
11.33/8.40	----------------------------------------
11.33/8.40	
11.33/8.40	(2)
11.33/8.40	BOUNDS(1, INF)
11.40/8.43	EOF