3.80/1.85	WORST_CASE(?, O(n^1))
3.80/1.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.80/1.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.80/1.86	
3.80/1.86	
3.80/1.86	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(3, 3 + Arg_0)).
3.80/1.86	
3.80/1.86	(0) CpxIntTrs
3.80/1.86	(1) Koat2 Proof [FINISHED, 226 ms]
3.80/1.86	(2) BOUNDS(1, max(3, 3 + Arg_0))
3.80/1.86	
3.80/1.86	
3.80/1.86	----------------------------------------
3.80/1.86	
3.80/1.86	(0)
3.80/1.86	Obligation:
3.80/1.86	Complexity Int TRS consisting of the following rules:
3.80/1.86	f2(A, B, C) -> Com_1(f2(-(B) + A, 1 + B, C)) :|: A >= 1
3.80/1.86	f3(A, B, C) -> Com_1(f2(A, B, C)) :|: B >= 1
3.80/1.86	f2(A, B, C) -> Com_1(f4(A, B, D)) :|: 0 >= A
3.80/1.86	f3(A, B, C) -> Com_1(f4(A, B, D)) :|: 0 >= B
3.80/1.86	
3.80/1.86	The start-symbols are:[f3_3]
3.80/1.86	
3.80/1.86	
3.80/1.86	----------------------------------------
3.80/1.86	
3.80/1.86	(1) Koat2 Proof (FINISHED)
3.80/1.86	YES( ?, max([3, 3+Arg_0]) {O(n)})
3.80/1.86	
3.80/1.86	
3.80/1.86	
3.80/1.86	Initial Complexity Problem:
3.80/1.86	
3.80/1.86	  Start:  f3  
3.80/1.86	
3.80/1.86	  Program_Vars:  Arg_0, Arg_1, Arg_2  
3.80/1.86	
3.80/1.86	  Temp_Vars:  D  
3.80/1.86	
3.80/1.86	  Locations:  f2, f3, f4  
3.80/1.86	
3.80/1.86	  Transitions:
3.80/1.86	
3.80/1.86	  f2(Arg_0,Arg_1,Arg_2) -> f2(-Arg_1+Arg_0,1+Arg_1,Arg_2):|:1 <= Arg_1 && 1 <= Arg_0
3.80/1.86	
3.80/1.86	  f2(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,D):|:1 <= Arg_1 && Arg_0 <= 0
3.80/1.86	
3.80/1.86	  f3(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2):|:1 <= Arg_1
3.80/1.86	
3.80/1.86	  f3(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,D):|:Arg_1 <= 0  
3.80/1.86	
3.80/1.86	
3.80/1.86	
3.80/1.86	Timebounds: 
3.80/1.86	
3.80/1.86	  Overall timebound: max([3, 3+Arg_0]) {O(n)}
3.80/1.86	
3.80/1.86	  0: f2->f2: max([0, Arg_0]) {O(n)}
3.80/1.86	
3.80/1.86	  2: f2->f4: 1 {O(1)}
3.80/1.86	
3.80/1.86	  1: f3->f2: 1 {O(1)}
3.80/1.86	
3.80/1.86	  3: f3->f4: 1 {O(1)}
3.80/1.86	
3.80/1.86	
3.80/1.86	
3.80/1.86	Costbounds:
3.80/1.86	
3.80/1.86	  Overall costbound: max([3, 3+Arg_0]) {O(n)}
3.80/1.86	
3.80/1.86	  0: f2->f2: max([0, Arg_0]) {O(n)}
3.80/1.86	
3.80/1.86	  2: f2->f4: 1 {O(1)}
3.80/1.86	
3.80/1.86	  1: f3->f2: 1 {O(1)}
3.80/1.86	
3.80/1.86	  3: f3->f4: 1 {O(1)}
3.80/1.86	
3.80/1.86	
3.80/1.86	
3.80/1.86	Sizebounds:
3.80/1.86	
3.80/1.86	`Lower:
3.80/1.86	
3.80/1.86	  0: f2->f2, Arg_1: 2 {O(1)}
3.80/1.86	
3.80/1.86	  0: f2->f2, Arg_2: Arg_2 {O(n)}
3.80/1.86	
3.80/1.86	  2: f2->f4, Arg_1: 1 {O(1)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_0: Arg_0 {O(n)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_1: 1 {O(1)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_2: Arg_2 {O(n)}
3.80/1.86	
3.80/1.86	  3: f3->f4, Arg_0: Arg_0 {O(n)}
3.80/1.86	
3.80/1.86	  3: f3->f4, Arg_1: Arg_1 {O(n)}
3.80/1.86	
3.80/1.86	`Upper:
3.80/1.86	
3.80/1.86	  0: f2->f2, Arg_0: Arg_0 {O(n)}
3.80/1.86	
3.80/1.86	  0: f2->f2, Arg_1: Arg_1+max([0, Arg_0]) {O(n)}
3.80/1.86	
3.80/1.86	  0: f2->f2, Arg_2: Arg_2 {O(n)}
3.80/1.86	
3.80/1.86	  2: f2->f4, Arg_0: 0 {O(1)}
3.80/1.86	
3.80/1.86	  2: f2->f4, Arg_1: max([Arg_1, Arg_1+max([0, Arg_0])]) {O(n)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_0: Arg_0 {O(n)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_1: Arg_1 {O(n)}
3.80/1.86	
3.80/1.86	  1: f3->f2, Arg_2: Arg_2 {O(n)}
3.80/1.86	
3.80/1.86	  3: f3->f4, Arg_0: Arg_0 {O(n)}
3.80/1.86	
3.80/1.86	  3: f3->f4, Arg_1: 0 {O(1)}
3.80/1.86	
3.80/1.86	
3.80/1.86	----------------------------------------
3.80/1.86	
3.80/1.86	(2)
3.80/1.86	BOUNDS(1, max(3, 3 + Arg_0))
3.80/1.88	EOF