3.73/1.80	WORST_CASE(?, O(n^1))
3.79/1.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.79/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.79/1.81	
3.79/1.81	
3.79/1.81	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(1, 1 + Arg_1)).
3.79/1.81	
3.79/1.81	(0) CpxIntTrs
3.79/1.81	(1) Koat2 Proof [FINISHED, 40 ms]
3.79/1.81	(2) BOUNDS(1, max(1, 1 + Arg_1))
3.79/1.81	
3.79/1.81	
3.79/1.81	----------------------------------------
3.79/1.81	
3.79/1.81	(0)
3.79/1.81	Obligation:
3.79/1.81	Complexity Int TRS consisting of the following rules:
3.79/1.81	f0(A, B) -> Com_1(f1(A, B)) :|: A >= 1
3.79/1.81	f1(A, B) -> Com_1(f1(1 + A, -(A) + B)) :|: B >= 1
3.79/1.81	
3.79/1.81	The start-symbols are:[f0_2]
3.79/1.81	
3.79/1.81	
3.79/1.81	----------------------------------------
3.79/1.81	
3.79/1.81	(1) Koat2 Proof (FINISHED)
3.79/1.81	YES( ?, max([1, 1+Arg_1]) {O(n)})
3.79/1.81	
3.79/1.81	
3.79/1.81	
3.79/1.81	Initial Complexity Problem:
3.79/1.81	
3.79/1.81	  Start:  f0  
3.79/1.81	
3.79/1.81	  Program_Vars:  Arg_0, Arg_1  
3.79/1.81	
3.79/1.81	  Temp_Vars:    
3.79/1.81	
3.79/1.81	  Locations:  f0, f1  
3.79/1.81	
3.79/1.81	  Transitions:
3.79/1.81	
3.79/1.81	  f0(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1 <= Arg_0
3.79/1.81	
3.79/1.81	  f1(Arg_0,Arg_1) -> f1(1+Arg_0,-Arg_0+Arg_1):|:1 <= Arg_0 && 1 <= Arg_1  
3.79/1.81	
3.79/1.81	
3.79/1.81	
3.79/1.81	Timebounds: 
3.79/1.81	
3.79/1.81	  Overall timebound: max([1, 1+Arg_1]) {O(n)}
3.79/1.81	
3.79/1.81	  0: f0->f1: 1 {O(1)}
3.79/1.81	
3.79/1.81	  1: f1->f1: max([0, Arg_1]) {O(n)}
3.79/1.81	
3.79/1.81	
3.79/1.81	
3.79/1.81	Costbounds:
3.79/1.81	
3.79/1.81	  Overall costbound: max([1, 1+Arg_1]) {O(n)}
3.79/1.81	
3.79/1.81	  0: f0->f1: 1 {O(1)}
3.79/1.81	
3.79/1.81	  1: f1->f1: max([0, Arg_1]) {O(n)}
3.79/1.81	
3.79/1.81	
3.79/1.81	
3.79/1.81	Sizebounds:
3.79/1.81	
3.79/1.81	`Lower:
3.79/1.81	
3.79/1.81	  0: f0->f1, Arg_0: 1 {O(1)}
3.79/1.81	
3.79/1.81	  0: f0->f1, Arg_1: Arg_1 {O(n)}
3.79/1.81	
3.79/1.81	  1: f1->f1, Arg_0: 2 {O(1)}
3.79/1.81	
3.79/1.81	`Upper:
3.79/1.81	
3.79/1.81	  0: f0->f1, Arg_0: Arg_0 {O(n)}
3.79/1.81	
3.79/1.81	  0: f0->f1, Arg_1: Arg_1 {O(n)}
3.79/1.81	
3.79/1.81	  1: f1->f1, Arg_0: Arg_0+max([0, Arg_1]) {O(n)}
3.79/1.81	
3.79/1.81	  1: f1->f1, Arg_1: Arg_1 {O(n)}
3.79/1.81	
3.79/1.81	
3.79/1.81	----------------------------------------
3.79/1.81	
3.79/1.81	(2)
3.79/1.81	BOUNDS(1, max(1, 1 + Arg_1))
3.81/1.85	EOF