4.10/2.16	WORST_CASE(?, O(n^1))
4.10/2.17	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.10/2.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.10/2.17	
4.10/2.17	
4.10/2.17	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)).
4.10/2.17	
4.10/2.17	(0) CpxIntTrs
4.10/2.17	(1) Koat2 Proof [FINISHED, 481 ms]
4.10/2.17	(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))
4.10/2.17	
4.10/2.17	
4.10/2.17	----------------------------------------
4.10/2.17	
4.10/2.17	(0)
4.10/2.17	Obligation:
4.10/2.17	Complexity Int TRS consisting of the following rules:
4.10/2.17	evalterminatestart(A, B, C) -> Com_1(evalterminateentryin(A, B, C)) :|: TRUE
4.10/2.17	evalterminateentryin(A, B, C) -> Com_1(evalterminatebb1in(B, A, C)) :|: TRUE
4.10/2.17	evalterminatebb1in(A, B, C) -> Com_1(evalterminatebbin(A, B, C)) :|: 100 >= B && A >= C
4.10/2.17	evalterminatebb1in(A, B, C) -> Com_1(evalterminatereturnin(A, B, C)) :|: B >= 101
4.10/2.17	evalterminatebb1in(A, B, C) -> Com_1(evalterminatereturnin(A, B, C)) :|: C >= A + 1
4.10/2.17	evalterminatebbin(A, B, C) -> Com_1(evalterminatebb1in(A - 1, C, B + 1)) :|: TRUE
4.10/2.17	evalterminatereturnin(A, B, C) -> Com_1(evalterminatestop(A, B, C)) :|: TRUE
4.10/2.17	
4.10/2.17	The start-symbols are:[evalterminatestart_3]
4.10/2.17	
4.10/2.17	
4.10/2.17	----------------------------------------
4.10/2.17	
4.10/2.17	(1) Koat2 Proof (FINISHED)
4.10/2.17	YES( ?, 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)})
4.10/2.17	
4.10/2.17	
4.10/2.17	
4.10/2.17	Initial Complexity Problem:
4.10/2.17	
4.10/2.17	  Start:  evalterminatestart  
4.10/2.17	
4.10/2.17	  Program_Vars:  Arg_0, Arg_1, Arg_2  
4.10/2.17	
4.10/2.17	  Temp_Vars:    
4.10/2.17	
4.10/2.17	  Locations:  evalterminatebb1in, evalterminatebbin, evalterminateentryin, evalterminatereturnin, evalterminatestart, evalterminatestop  
4.10/2.17	
4.10/2.17	  Transitions:
4.10/2.17	
4.10/2.17	  evalterminatebb1in(Arg_0,Arg_1,Arg_2) -> evalterminatebbin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 100 && Arg_2 <= Arg_0
4.10/2.17	
4.10/2.17	  evalterminatebb1in(Arg_0,Arg_1,Arg_2) -> evalterminatereturnin(Arg_0,Arg_1,Arg_2):|:101 <= Arg_1
4.10/2.17	
4.10/2.17	  evalterminatebb1in(Arg_0,Arg_1,Arg_2) -> evalterminatereturnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1 <= Arg_2
4.10/2.17	
4.10/2.17	  evalterminatebbin(Arg_0,Arg_1,Arg_2) -> evalterminatebb1in(Arg_0-1,Arg_2,Arg_1+1):|:Arg_2 <= Arg_0 && Arg_1 <= 100
4.10/2.17	
4.10/2.17	  evalterminateentryin(Arg_0,Arg_1,Arg_2) -> evalterminatebb1in(Arg_1,Arg_0,Arg_2):|:
4.10/2.17	
4.10/2.17	  evalterminatereturnin(Arg_0,Arg_1,Arg_2) -> evalterminatestop(Arg_0,Arg_1,Arg_2):|:
4.10/2.17	
4.10/2.17	  evalterminatestart(Arg_0,Arg_1,Arg_2) -> evalterminateentryin(Arg_0,Arg_1,Arg_2):|:  
4.10/2.17	
4.10/2.17	
4.10/2.17	
4.10/2.17	Timebounds: 
4.10/2.17	
4.10/2.17	  Overall timebound: 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in: max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in: 1 {O(1)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop: 1 {O(1)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin: 1 {O(1)}
4.10/2.17	
4.10/2.17	
4.10/2.17	
4.10/2.17	Costbounds:
4.10/2.17	
4.10/2.17	  Overall costbound: 3+max([0, 102+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in: max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in: 1 {O(1)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop: 1 {O(1)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin: 1 {O(1)}
4.10/2.17	
4.10/2.17	
4.10/2.17	
4.10/2.17	Sizebounds:
4.10/2.17	
4.10/2.17	`Lower:
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_0: Arg_1-max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_1: min([Arg_2, Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_2: min([Arg_2, Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_1: 101 {O(1)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_1: min([Arg_0, min([Arg_2, Arg_0])]) {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_0: Arg_1-max([0, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_1: min([Arg_2, Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_2: min([Arg_2, Arg_0]) {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_1: Arg_0 {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_2: Arg_2 {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 102+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_1: min([101, min([Arg_2, Arg_0])]) {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_0: Arg_0 {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_1: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_2: Arg_2 {O(n)}
4.10/2.17	
4.10/2.17	`Upper:
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_1: 100 {O(1)}
4.10/2.17	
4.10/2.17	  2: evalterminatebb1in->evalterminatebbin, Arg_2: max([101, Arg_2]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.10/2.17	
4.10/2.17	  3: evalterminatebb1in->evalterminatereturnin, Arg_2: max([101, Arg_2]) {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.10/2.17	
4.10/2.17	  4: evalterminatebb1in->evalterminatereturnin, Arg_2: max([101, Arg_2]) {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_1: max([101, Arg_2]) {O(n)}
4.10/2.17	
4.10/2.17	  5: evalterminatebbin->evalterminatebb1in, Arg_2: 101 {O(1)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_1: Arg_0 {O(n)}
4.10/2.17	
4.10/2.17	  1: evalterminateentryin->evalterminatebb1in, Arg_2: Arg_2 {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_0: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}
4.10/2.17	
4.10/2.17	  6: evalterminatereturnin->evalterminatestop, Arg_2: max([101, Arg_2]) {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_0: Arg_0 {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_1: Arg_1 {O(n)}
4.10/2.17	
4.10/2.17	  0: evalterminatestart->evalterminateentryin, Arg_2: Arg_2 {O(n)}
4.10/2.17	
4.10/2.17	
4.10/2.17	----------------------------------------
4.10/2.17	
4.10/2.17	(2)
4.10/2.17	BOUNDS(1, max(3, 105 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))
4.24/2.20	EOF