3.52/1.72	WORST_CASE(?, O(1))
3.52/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.52/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.52/1.72	
3.52/1.72	
3.52/1.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.52/1.72	
3.52/1.72	(0) CpxIntTrs
3.52/1.72	(1) Koat2 Proof [FINISHED, 39 ms]
3.52/1.72	(2) BOUNDS(1, 1)
3.52/1.72	
3.52/1.72	
3.52/1.72	----------------------------------------
3.52/1.72	
3.52/1.72	(0)
3.52/1.72	Obligation:
3.52/1.72	Complexity Int TRS consisting of the following rules:
3.52/1.72	f0(A) -> Com_1(f5(B)) :|: B >= 1
3.52/1.72	f5(A) -> Com_1(f5(A + 1)) :|: 19 >= A
3.52/1.72	f0(A) -> Com_1(f12(B)) :|: 0 >= B
3.52/1.72	f5(A) -> Com_1(f12(A)) :|: A >= 20
3.52/1.72	
3.52/1.72	The start-symbols are:[f0_1]
3.52/1.72	
3.52/1.72	
3.52/1.72	----------------------------------------
3.52/1.72	
3.52/1.72	(1) Koat2 Proof (FINISHED)
3.52/1.72	YES( ?, 22 {O(1)})
3.52/1.72	
3.52/1.72	
3.52/1.72	
3.52/1.72	Initial Complexity Problem:
3.52/1.72	
3.52/1.72	  Start:  f0  
3.52/1.72	
3.52/1.72	  Program_Vars:  Arg_0  
3.52/1.72	
3.52/1.72	  Temp_Vars:  B  
3.52/1.72	
3.52/1.72	  Locations:  f0, f12, f5  
3.52/1.72	
3.52/1.72	  Transitions:
3.52/1.72	
3.52/1.72	  f0(Arg_0) -> f12(B):|:B <= 0
3.52/1.72	
3.52/1.72	  f0(Arg_0) -> f5(B):|:1 <= B
3.52/1.72	
3.52/1.72	  f5(Arg_0) -> f12(Arg_0):|:1 <= Arg_0 && 20 <= Arg_0
3.52/1.72	
3.52/1.72	  f5(Arg_0) -> f5(Arg_0+1):|:1 <= Arg_0 && Arg_0 <= 19  
3.52/1.72	
3.52/1.72	
3.52/1.72	
3.52/1.72	Timebounds: 
3.52/1.72	
3.52/1.72	  Overall timebound: 22 {O(1)}
3.52/1.72	
3.52/1.72	  0: f0->f5: 1 {O(1)}
3.52/1.72	
3.52/1.72	  2: f0->f12: 1 {O(1)}
3.52/1.72	
3.52/1.72	  1: f5->f5: 19 {O(1)}
3.52/1.72	
3.52/1.72	  3: f5->f12: 1 {O(1)}
3.52/1.72	
3.52/1.72	
3.52/1.72	
3.52/1.72	Costbounds:
3.52/1.72	
3.52/1.72	  Overall costbound: 22 {O(1)}
3.52/1.72	
3.52/1.72	  0: f0->f5: 1 {O(1)}
3.52/1.72	
3.52/1.72	  2: f0->f12: 1 {O(1)}
3.52/1.72	
3.52/1.72	  1: f5->f5: 19 {O(1)}
3.52/1.72	
3.52/1.72	  3: f5->f12: 1 {O(1)}
3.52/1.72	
3.52/1.72	
3.52/1.72	
3.52/1.72	Sizebounds:
3.52/1.72	
3.52/1.72	`Lower:
3.52/1.72	
3.52/1.72	  0: f0->f5, Arg_0: 1 {O(1)}
3.52/1.72	
3.52/1.72	  1: f5->f5, Arg_0: 2 {O(1)}
3.52/1.72	
3.52/1.72	  3: f5->f12, Arg_0: 20 {O(1)}
3.52/1.72	
3.52/1.72	`Upper:
3.52/1.72	
3.52/1.72	  2: f0->f12, Arg_0: 0 {O(1)}
3.52/1.72	
3.52/1.72	  1: f5->f5, Arg_0: 20 {O(1)}
3.52/1.72	
3.52/1.72	
3.52/1.72	----------------------------------------
3.52/1.72	
3.52/1.72	(2)
3.52/1.72	BOUNDS(1, 1)
3.62/1.76	EOF