4.24/2.13	WORST_CASE(?, O(n^1))
4.24/2.14	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.24/2.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.24/2.14	
4.24/2.14	
4.24/2.14	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(3, 3 + Arg_0 + -1 * Arg_1)).
4.24/2.14	
4.24/2.14	(0) CpxIntTrs
4.24/2.14	(1) Koat2 Proof [FINISHED, 416 ms]
4.24/2.14	(2) BOUNDS(1, max(3, 3 + Arg_0 + -1 * Arg_1))
4.24/2.14	
4.24/2.14	
4.24/2.14	----------------------------------------
4.24/2.14	
4.24/2.14	(0)
4.24/2.14	Obligation:
4.24/2.14	Complexity Int TRS consisting of the following rules:
4.24/2.14	f4(A, B, C, D, E, F, G) -> Com_1(f4(A + B, B, C, D, E, F, G)) :|: A >= 0
4.24/2.14	f4(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: 0 >= A + 1
4.24/2.14	f5(A, B, C, D, E, F, G) -> Com_1(f4(A, B, C, D, E, F, G)) :|: 0 >= B + 1
4.24/2.14	f5(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: B >= 0
4.24/2.14	
4.24/2.14	The start-symbols are:[f5_7]
4.24/2.14	
4.24/2.14	
4.24/2.14	----------------------------------------
4.24/2.14	
4.24/2.14	(1) Koat2 Proof (FINISHED)
4.24/2.14	YES( ?, max([3, 3+Arg_0-Arg_1]) {O(n)})
4.24/2.14	
4.24/2.14	
4.24/2.14	
4.24/2.14	Initial Complexity Problem:
4.24/2.14	
4.24/2.14	  Start:  f5  
4.24/2.14	
4.24/2.14	  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6  
4.24/2.14	
4.24/2.14	  Temp_Vars:    
4.24/2.14	
4.24/2.14	  Locations:  f4, f5, f6  
4.24/2.14	
4.24/2.14	  Transitions:
4.24/2.14	
4.24/2.14	  f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:1+Arg_1 <= 0 && 0 <= Arg_0
4.24/2.14	
4.24/2.14	  f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:1+Arg_1 <= 0 && Arg_0+1 <= 0
4.24/2.14	
4.24/2.14	  f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1+1 <= 0
4.24/2.14	
4.24/2.14	  f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:0 <= Arg_1  
4.24/2.14	
4.24/2.14	
4.24/2.14	
4.24/2.14	Timebounds: 
4.24/2.14	
4.24/2.14	  Overall timebound: max([3, 3+Arg_0-Arg_1]) {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4: max([0, Arg_0-Arg_1]) {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6: 1 {O(1)}
4.24/2.14	
4.24/2.14	  2: f5->f4: 1 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6: 1 {O(1)}
4.24/2.14	
4.24/2.14	
4.24/2.14	
4.24/2.14	Costbounds:
4.24/2.14	
4.24/2.14	  Overall costbound: max([3, 3+Arg_0-Arg_1]) {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4: max([0, Arg_0-Arg_1]) {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6: 1 {O(1)}
4.24/2.14	
4.24/2.14	  2: f5->f4: 1 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6: 1 {O(1)}
4.24/2.14	
4.24/2.14	
4.24/2.14	
4.24/2.14	Sizebounds:
4.24/2.14	
4.24/2.14	`Lower:
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_0: Arg_1 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_1: Arg_1 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_2: Arg_2 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_3: Arg_3 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_4: Arg_4 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_5: Arg_5 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_6: Arg_6 {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_0: min([Arg_0, Arg_1]) {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_1: Arg_1 {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_2: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_3: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_4: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_5: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_6: 0 {O(1)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_0: Arg_0 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_1: Arg_1 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_2: Arg_2 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_3: Arg_3 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_4: Arg_4 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_5: Arg_5 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_6: Arg_6 {O(n)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_0: Arg_0 {O(n)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_1: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_2: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_3: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_4: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_5: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_6: 0 {O(1)}
4.24/2.14	
4.24/2.14	`Upper:
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_0: Arg_0 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_1: -1 {O(1)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_2: Arg_2 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_3: Arg_3 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_4: Arg_4 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_5: Arg_5 {O(n)}
4.24/2.14	
4.24/2.14	  0: f4->f4, Arg_6: Arg_6 {O(n)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_0: -1 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_1: -1 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_2: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_3: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_4: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_5: 0 {O(1)}
4.24/2.14	
4.24/2.14	  1: f4->f6, Arg_6: 0 {O(1)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_0: Arg_0 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_1: -1 {O(1)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_2: Arg_2 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_3: Arg_3 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_4: Arg_4 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_5: Arg_5 {O(n)}
4.24/2.14	
4.24/2.14	  2: f5->f4, Arg_6: Arg_6 {O(n)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_0: Arg_0 {O(n)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_1: Arg_1 {O(n)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_2: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_3: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_4: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_5: 0 {O(1)}
4.24/2.14	
4.24/2.14	  3: f5->f6, Arg_6: 0 {O(1)}
4.24/2.14	
4.24/2.14	
4.24/2.14	----------------------------------------
4.24/2.14	
4.24/2.14	(2)
4.24/2.14	BOUNDS(1, max(3, 3 + Arg_0 + -1 * Arg_1))
4.29/2.42	EOF