3.64/1.77	WORST_CASE(?, O(n^1))
3.64/1.78	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.64/1.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.64/1.78	
3.64/1.78	
3.64/1.78	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(1, 102 + -1 * Arg_0 + Arg_1 + -1 * Arg_2)).
3.64/1.78	
3.64/1.78	(0) CpxIntTrs
3.64/1.78	(1) Koat2 Proof [FINISHED, 137 ms]
3.64/1.78	(2) BOUNDS(1, max(1, 102 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))
3.64/1.78	
3.64/1.78	
3.64/1.78	----------------------------------------
3.64/1.78	
3.64/1.78	(0)
3.64/1.78	Obligation:
3.64/1.78	Complexity Int TRS consisting of the following rules:
3.64/1.78	eval(A, B, C) -> Com_1(eval(C, B - 1, A + 1)) :|: 100 >= A && B >= C
3.64/1.78	start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE
3.64/1.78	
3.64/1.78	The start-symbols are:[start_3]
3.64/1.78	
3.64/1.78	
3.64/1.78	----------------------------------------
3.64/1.78	
3.64/1.78	(1) Koat2 Proof (FINISHED)
3.64/1.78	YES( ?, max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)})
3.64/1.78	
3.64/1.78	
3.64/1.78	
3.64/1.78	Initial Complexity Problem:
3.64/1.78	
3.64/1.78	  Start:  start  
3.64/1.78	
3.64/1.78	  Program_Vars:  Arg_0, Arg_1, Arg_2  
3.64/1.78	
3.64/1.78	  Temp_Vars:    
3.64/1.78	
3.64/1.78	  Locations:  eval, start  
3.64/1.78	
3.64/1.78	  Transitions:
3.64/1.78	
3.64/1.78	  eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_2,Arg_1-1,Arg_0+1):|:Arg_0 <= 100 && Arg_2 <= Arg_1
3.64/1.78	
3.64/1.78	  start(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2):|:  
3.64/1.78	
3.64/1.78	
3.64/1.78	
3.64/1.78	Timebounds: 
3.64/1.78	
3.64/1.78	  Overall timebound: max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval: 1 {O(1)}
3.64/1.78	
3.64/1.78	
3.64/1.78	
3.64/1.78	Costbounds:
3.64/1.78	
3.64/1.78	  Overall costbound: max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval: 1 {O(1)}
3.64/1.78	
3.64/1.78	
3.64/1.78	
3.64/1.78	Sizebounds:
3.64/1.78	
3.64/1.78	`Lower:
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_0: min([Arg_0, Arg_2]) {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_1: Arg_1-max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_2: min([Arg_0, Arg_2]) {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_0: Arg_0 {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_1: Arg_1 {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_2: Arg_2 {O(n)}
3.64/1.78	
3.64/1.78	`Upper:
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_0: max([101, Arg_2]) {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_1: Arg_1 {O(n)}
3.64/1.78	
3.64/1.78	  0: eval->eval, Arg_2: 101 {O(1)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_0: Arg_0 {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_1: Arg_1 {O(n)}
3.64/1.78	
3.64/1.78	  1: start->eval, Arg_2: Arg_2 {O(n)}
3.64/1.78	
3.64/1.78	
3.64/1.78	----------------------------------------
3.64/1.78	
3.64/1.78	(2)
3.64/1.78	BOUNDS(1, max(1, 102 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))
3.64/1.82	EOF