3.92/2.04	WORST_CASE(?, O(n^1))
3.92/2.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.92/2.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/2.05	
3.92/2.05	
3.92/2.05	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(103, 2 + 101 * Arg_1)).
3.92/2.05	
3.92/2.05	(0) CpxIntTrs
3.92/2.05	(1) Koat2 Proof [FINISHED, 340 ms]
3.92/2.05	(2) BOUNDS(1, max(103, 2 + 101 * Arg_1))
3.92/2.05	
3.92/2.05	
3.92/2.05	----------------------------------------
3.92/2.05	
3.92/2.05	(0)
3.92/2.05	Obligation:
3.92/2.05	Complexity Int TRS consisting of the following rules:
3.92/2.05	f300(A, B, C, D, E) -> Com_1(f300(1 + A, B, C, D, E)) :|: 100 >= A && B >= 1
3.92/2.05	f300(A, B, C, D, E) -> Com_1(f3(A, B, 0, 0, 0)) :|: A >= 101
3.92/2.05	f2(A, B, C, D, E) -> Com_1(f300(1, B, C, D, E)) :|: B >= 1
3.92/2.05	f2(A, B, C, D, E) -> Com_1(f3(0, B, 0, 0, 0)) :|: 0 >= B
3.92/2.05	
3.92/2.05	The start-symbols are:[f2_5]
3.92/2.05	
3.92/2.05	
3.92/2.05	----------------------------------------
3.92/2.05	
3.92/2.05	(1) Koat2 Proof (FINISHED)
3.92/2.05	YES( ?, max([103, 2+101*Arg_1]) {O(n)})
3.92/2.05	
3.92/2.05	
3.92/2.05	
3.92/2.05	Initial Complexity Problem:
3.92/2.05	
3.92/2.05	  Start:  f2  
3.92/2.05	
3.92/2.05	  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4  
3.92/2.05	
3.92/2.05	  Temp_Vars:    
3.92/2.05	
3.92/2.05	  Locations:  f2, f3, f300  
3.92/2.05	
3.92/2.05	  Transitions:
3.92/2.05	
3.92/2.05	  f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f3(0,Arg_1,0,0,0):|:Arg_1 <= 0
3.92/2.05	
3.92/2.05	  f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f300(1,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_1
3.92/2.05	
3.92/2.05	  f300(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f3(Arg_0,Arg_1,0,0,0):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && 101 <= Arg_0
3.92/2.05	
3.92/2.05	  f300(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f300(1+Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_0 <= 100 && 1 <= Arg_1  
3.92/2.05	
3.92/2.05	
3.92/2.05	
3.92/2.05	Timebounds: 
3.92/2.05	
3.92/2.05	  Overall timebound: max([103, 2+101*Arg_1]) {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300: 1 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3: 1 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300: max([100, -1+101*Arg_1]) {O(n)}
3.92/2.05	
3.92/2.05	  1: f300->f3: 1 {O(1)}
3.92/2.05	
3.92/2.05	
3.92/2.05	
3.92/2.05	Costbounds:
3.92/2.05	
3.92/2.05	  Overall costbound: max([103, 2+101*Arg_1]) {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300: 1 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3: 1 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300: max([100, -1+101*Arg_1]) {O(n)}
3.92/2.05	
3.92/2.05	  1: f300->f3: 1 {O(1)}
3.92/2.05	
3.92/2.05	
3.92/2.05	
3.92/2.05	Sizebounds:
3.92/2.05	
3.92/2.05	`Lower:
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_0: 1 {O(1)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_1: 1 {O(1)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_2: Arg_2 {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_3: Arg_3 {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_4: Arg_4 {O(n)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_0: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_1: Arg_1 {O(n)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_2: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_3: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_4: 0 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_0: 2 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_1: 1 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_2: Arg_2 {O(n)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_3: Arg_3 {O(n)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_4: Arg_4 {O(n)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_0: 101 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_1: 1 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_2: 0 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_3: 0 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_4: 0 {O(1)}
3.92/2.05	
3.92/2.05	`Upper:
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_0: 1 {O(1)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_1: Arg_1 {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_2: Arg_2 {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_3: Arg_3 {O(n)}
3.92/2.05	
3.92/2.05	  2: f2->f300, Arg_4: Arg_4 {O(n)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_0: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_1: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_2: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_3: 0 {O(1)}
3.92/2.05	
3.92/2.05	  3: f2->f3, Arg_4: 0 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_0: 101 {O(1)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_1: Arg_1 {O(n)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_2: Arg_2 {O(n)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_3: Arg_3 {O(n)}
3.92/2.05	
3.92/2.05	  0: f300->f300, Arg_4: Arg_4 {O(n)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_0: 101 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_1: Arg_1 {O(n)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_2: 0 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_3: 0 {O(1)}
3.92/2.05	
3.92/2.05	  1: f300->f3, Arg_4: 0 {O(1)}
3.92/2.05	
3.92/2.05	
3.92/2.05	----------------------------------------
3.92/2.05	
3.92/2.05	(2)
3.92/2.05	BOUNDS(1, max(103, 2 + 101 * Arg_1))
3.92/2.07	EOF