4.07/2.12	WORST_CASE(?, O(n^1))
4.07/2.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.07/2.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.07/2.13	
4.07/2.13	
4.07/2.13	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(3, 105 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2)).
4.07/2.13	
4.07/2.13	(0) CpxIntTrs
4.07/2.13	(1) Koat2 Proof [FINISHED, 459 ms]
4.07/2.13	(2) BOUNDS(1, max(3, 105 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))
4.07/2.13	
4.07/2.13	
4.07/2.13	----------------------------------------
4.07/2.13	
4.07/2.13	(0)
4.07/2.13	Obligation:
4.07/2.13	Complexity Int TRS consisting of the following rules:
4.07/2.13	evalexministart(A, B, C) -> Com_1(evalexminientryin(A, B, C)) :|: TRUE
4.07/2.13	evalexminientryin(A, B, C) -> Com_1(evalexminibb1in(B, A, C)) :|: TRUE
4.07/2.13	evalexminibb1in(A, B, C) -> Com_1(evalexminibbin(A, B, C)) :|: 100 >= B && A >= C
4.07/2.13	evalexminibb1in(A, B, C) -> Com_1(evalexminireturnin(A, B, C)) :|: B >= 101
4.07/2.13	evalexminibb1in(A, B, C) -> Com_1(evalexminireturnin(A, B, C)) :|: C >= A + 1
4.07/2.13	evalexminibbin(A, B, C) -> Com_1(evalexminibb1in(A - 1, C, B + 1)) :|: TRUE
4.07/2.13	evalexminireturnin(A, B, C) -> Com_1(evalexministop(A, B, C)) :|: TRUE
4.07/2.13	
4.07/2.13	The start-symbols are:[evalexministart_3]
4.07/2.13	
4.07/2.13	
4.07/2.13	----------------------------------------
4.07/2.13	
4.07/2.13	(1) Koat2 Proof (FINISHED)
4.07/2.13	YES( ?, 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)})
4.07/2.13	
4.07/2.13	
4.07/2.13	
4.07/2.13	Initial Complexity Problem:
4.07/2.13	
4.07/2.13	  Start:  evalexministart  
4.07/2.13	
4.07/2.13	  Program_Vars:  Arg_0, Arg_1, Arg_2  
4.07/2.13	
4.07/2.13	  Temp_Vars:    
4.07/2.13	
4.07/2.13	  Locations:  evalexminibb1in, evalexminibbin, evalexminientryin, evalexminireturnin, evalexministart, evalexministop  
4.07/2.13	
4.07/2.13	  Transitions:
4.07/2.13	
4.07/2.13	  evalexminibb1in(Arg_0,Arg_1,Arg_2) -> evalexminibbin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 100 && Arg_2 <= Arg_0
4.07/2.13	
4.07/2.13	  evalexminibb1in(Arg_0,Arg_1,Arg_2) -> evalexminireturnin(Arg_0,Arg_1,Arg_2):|:101 <= Arg_1
4.07/2.13	
4.07/2.13	  evalexminibb1in(Arg_0,Arg_1,Arg_2) -> evalexminireturnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1 <= Arg_2
4.07/2.13	
4.07/2.13	  evalexminibbin(Arg_0,Arg_1,Arg_2) -> evalexminibb1in(Arg_0-1,Arg_2,Arg_1+1):|:Arg_2 <= Arg_0 && Arg_1 <= 100
4.07/2.13	
4.07/2.13	  evalexminientryin(Arg_0,Arg_1,Arg_2) -> evalexminibb1in(Arg_1,Arg_0,Arg_2):|:
4.07/2.13	
4.07/2.13	  evalexminireturnin(Arg_0,Arg_1,Arg_2) -> evalexministop(Arg_0,Arg_1,Arg_2):|:
4.07/2.13	
4.07/2.13	  evalexministart(Arg_0,Arg_1,Arg_2) -> evalexminientryin(Arg_0,Arg_1,Arg_2):|:  
4.07/2.13	
4.07/2.13	
4.07/2.13	
4.07/2.13	Timebounds: 
4.07/2.13	
4.07/2.13	  Overall timebound: 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin: 1 {O(1)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin: 1 {O(1)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in: max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in: 1 {O(1)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop: 1 {O(1)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin: 1 {O(1)}
4.07/2.13	
4.07/2.13	
4.07/2.13	
4.07/2.13	Costbounds:
4.07/2.13	
4.07/2.13	  Overall costbound: 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin: 1 {O(1)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin: 1 {O(1)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in: max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in: 1 {O(1)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop: 1 {O(1)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin: 1 {O(1)}
4.07/2.13	
4.07/2.13	
4.07/2.13	
4.07/2.13	Sizebounds:
4.07/2.13	
4.07/2.13	`Lower:
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_0: Arg_1-max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_1: min([Arg_2, Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_2: min([Arg_2, Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_1: 101 {O(1)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_1: min([Arg_0, min([Arg_2, Arg_0])]) {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_0: Arg_1-max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_1: min([Arg_2, Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_2: min([Arg_2, Arg_0]) {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_1: Arg_0 {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_2: Arg_2 {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_1: min([101, min([Arg_2, Arg_0])]) {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_0: Arg_0 {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_1: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_2: Arg_2 {O(n)}
4.07/2.13	
4.07/2.13	`Upper:
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_1: 100 {O(1)}
4.07/2.13	
4.07/2.13	  2: evalexminibb1in->evalexminibbin, Arg_2: max([101, Arg_2]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.07/2.13	
4.07/2.13	  3: evalexminibb1in->evalexminireturnin, Arg_2: max([101, Arg_2]) {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.07/2.13	
4.07/2.13	  4: evalexminibb1in->evalexminireturnin, Arg_2: max([101, Arg_2]) {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_1: max([101, Arg_2]) {O(n)}
4.07/2.13	
4.07/2.13	  5: evalexminibbin->evalexminibb1in, Arg_2: 101 {O(1)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_1: Arg_0 {O(n)}
4.07/2.13	
4.07/2.13	  1: evalexminientryin->evalexminibb1in, Arg_2: Arg_2 {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_0: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.07/2.13	
4.07/2.13	  6: evalexminireturnin->evalexministop, Arg_2: max([101, Arg_2]) {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_0: Arg_0 {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_1: Arg_1 {O(n)}
4.07/2.13	
4.07/2.13	  0: evalexministart->evalexminientryin, Arg_2: Arg_2 {O(n)}
4.07/2.13	
4.07/2.13	
4.07/2.13	----------------------------------------
4.07/2.13	
4.07/2.13	(2)
4.07/2.13	BOUNDS(1, max(3, 105 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))
4.07/2.16	EOF