5.29/2.46	WORST_CASE(Omega(n^1), O(n^1))
5.29/2.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.29/2.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.29/2.47	
5.29/2.47	
5.29/2.47	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(6, 6 + 2 * Arg_0) + max(1, 1 + 2 * Arg_0) + nat(Arg_0)).
5.29/2.47	
5.29/2.47	(0) CpxIntTrs
5.29/2.47	(1) Koat2 Proof [FINISHED, 826 ms]
5.29/2.47	(2) BOUNDS(1, max(6, 6 + 2 * Arg_0) + max(1, 1 + 2 * Arg_0) + nat(Arg_0))
5.29/2.47	(3) Loat Proof [FINISHED, 721 ms]
5.29/2.47	(4) BOUNDS(n^1, INF)
5.29/2.47	
5.29/2.47	
5.29/2.47	----------------------------------------
5.29/2.47	
5.29/2.47	(0)
5.29/2.47	Obligation:
5.29/2.47	Complexity Int TRS consisting of the following rules:
5.29/2.47	evalspeedpldi2start(A, B, C) -> Com_1(evalspeedpldi2entryin(A, B, C)) :|: TRUE
5.29/2.47	evalspeedpldi2entryin(A, B, C) -> Com_1(evalspeedpldi2bb5in(B, 0, A)) :|: A >= 0 && B >= 1
5.29/2.47	evalspeedpldi2entryin(A, B, C) -> Com_1(evalspeedpldi2returnin(A, B, C)) :|: 0 >= A + 1
5.29/2.47	evalspeedpldi2entryin(A, B, C) -> Com_1(evalspeedpldi2returnin(A, B, C)) :|: 0 >= B
5.29/2.47	evalspeedpldi2bb5in(A, B, C) -> Com_1(evalspeedpldi2bb2in(A, B, C)) :|: C >= 1
5.29/2.47	evalspeedpldi2bb5in(A, B, C) -> Com_1(evalspeedpldi2returnin(A, B, C)) :|: 0 >= C
5.29/2.47	evalspeedpldi2bb2in(A, B, C) -> Com_1(evalspeedpldi2bb3in(A, B, C)) :|: A >= B + 1
5.29/2.47	evalspeedpldi2bb2in(A, B, C) -> Com_1(evalspeedpldi2bb5in(A, 0, C)) :|: B >= A
5.29/2.47	evalspeedpldi2bb3in(A, B, C) -> Com_1(evalspeedpldi2bb5in(A, B + 1, C - 1)) :|: TRUE
5.29/2.47	evalspeedpldi2returnin(A, B, C) -> Com_1(evalspeedpldi2stop(A, B, C)) :|: TRUE
5.29/2.47	
5.29/2.47	The start-symbols are:[evalspeedpldi2start_3]
5.29/2.47	
5.29/2.47	
5.29/2.47	----------------------------------------
5.29/2.47	
5.29/2.47	(1) Koat2 Proof (FINISHED)
5.29/2.47	YES( ?, 6+2*max([0, Arg_0])+max([1, 1+2*Arg_0])+max([0, Arg_0]) {O(n)})
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Initial Complexity Problem:
5.29/2.47	
5.29/2.47	  Start:  evalspeedpldi2start  
5.29/2.47	
5.29/2.47	  Program_Vars:  Arg_0, Arg_1, Arg_2  
5.29/2.47	
5.29/2.47	  Temp_Vars:    
5.29/2.47	
5.29/2.47	  Locations:  evalspeedpldi2bb2in, evalspeedpldi2bb3in, evalspeedpldi2bb5in, evalspeedpldi2entryin, evalspeedpldi2returnin, evalspeedpldi2start, evalspeedpldi2stop  
5.29/2.47	
5.29/2.47	  Transitions:
5.29/2.47	
5.29/2.47	  evalspeedpldi2bb2in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2bb3in(Arg_0,Arg_1,Arg_2):|:1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1+1 <= Arg_0
5.29/2.47	
5.29/2.47	  evalspeedpldi2bb2in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2bb5in(Arg_0,0,Arg_2):|:1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_0 <= Arg_1
5.29/2.47	
5.29/2.47	  evalspeedpldi2bb3in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2bb5in(Arg_0,Arg_1+1,Arg_2-1):|:1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0
5.29/2.47	
5.29/2.47	  evalspeedpldi2bb5in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2bb2in(Arg_0,Arg_1,Arg_2):|:0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && 1 <= Arg_2
5.29/2.47	
5.29/2.47	  evalspeedpldi2bb5in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2returnin(Arg_0,Arg_1,Arg_2):|:0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_2 <= 0
5.29/2.47	
5.29/2.47	  evalspeedpldi2entryin(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2bb5in(Arg_1,0,Arg_0):|:0 <= Arg_0 && 1 <= Arg_1
5.29/2.47	
5.29/2.47	  evalspeedpldi2entryin(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2returnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1 <= 0
5.29/2.47	
5.29/2.47	  evalspeedpldi2entryin(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2returnin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0
5.29/2.47	
5.29/2.47	  evalspeedpldi2returnin(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2stop(Arg_0,Arg_1,Arg_2):|:
5.29/2.47	
5.29/2.47	  evalspeedpldi2start(Arg_0,Arg_1,Arg_2) -> evalspeedpldi2entryin(Arg_0,Arg_1,Arg_2):|:  
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Timebounds: 
5.29/2.47	
5.29/2.47	  Overall timebound: 6+2*max([0, Arg_0])+max([1, 1+2*Arg_0])+max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in: max([1, 1+2*Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in: 1 {O(1)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop: 1 {O(1)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin: 1 {O(1)}
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Costbounds:
5.29/2.47	
5.29/2.47	  Overall costbound: 6+2*max([0, Arg_0])+max([1, 1+2*Arg_0])+max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in: max([1, 1+2*Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in: 1 {O(1)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin: 1 {O(1)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop: 1 {O(1)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin: 1 {O(1)}
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Sizebounds:
5.29/2.47	
5.29/2.47	`Lower:
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_2: 1 {O(1)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_2: 1 {O(1)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_1: 1 {O(1)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_2: 0 {O(1)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_2: 1 {O(1)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_2: 0 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_0: 1 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_2: 0 {O(1)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_0: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_1: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_0: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_1: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_0: min([1, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_1: min([0, Arg_1]) {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_2: min([0, Arg_2]) {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_0: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_1: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	`Upper:
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_1: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  6: evalspeedpldi2bb2in->evalspeedpldi2bb3in, Arg_2: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  7: evalspeedpldi2bb2in->evalspeedpldi2bb5in, Arg_2: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_1: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  8: evalspeedpldi2bb3in->evalspeedpldi2bb5in, Arg_2: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_1: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  4: evalspeedpldi2bb5in->evalspeedpldi2bb2in, Arg_2: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_1: max([0, Arg_0]) {O(n)}
5.29/2.47	
5.29/2.47	  5: evalspeedpldi2bb5in->evalspeedpldi2returnin, Arg_2: 0 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_0: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  1: evalspeedpldi2entryin->evalspeedpldi2bb5in, Arg_2: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_0: -1 {O(1)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_1: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  2: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_0: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_1: 0 {O(1)}
5.29/2.47	
5.29/2.47	  3: evalspeedpldi2entryin->evalspeedpldi2returnin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_0: max([-1, max([Arg_1, Arg_0])]) {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_1: max([0, max([Arg_0, Arg_1])]) {O(n)}
5.29/2.47	
5.29/2.47	  9: evalspeedpldi2returnin->evalspeedpldi2stop, Arg_2: max([0, Arg_2]) {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_0: Arg_0 {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_1: Arg_1 {O(n)}
5.29/2.47	
5.29/2.47	  0: evalspeedpldi2start->evalspeedpldi2entryin, Arg_2: Arg_2 {O(n)}
5.29/2.47	
5.29/2.47	
5.29/2.47	----------------------------------------
5.29/2.47	
5.29/2.47	(2)
5.29/2.47	BOUNDS(1, max(6, 6 + 2 * Arg_0) + max(1, 1 + 2 * Arg_0) + nat(Arg_0))
5.29/2.47	
5.29/2.47	----------------------------------------
5.29/2.47	
5.29/2.47	(3) Loat Proof (FINISHED)
5.29/2.47	
5.29/2.47	
5.29/2.47	### Pre-processing the ITS problem ###
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Initial linear ITS problem
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	      0: evalspeedpldi2start -> evalspeedpldi2entryin : [], cost: 1
5.29/2.47	
5.29/2.47	      1: evalspeedpldi2entryin -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 1
5.29/2.47	
5.29/2.47	      2: evalspeedpldi2entryin -> evalspeedpldi2returnin : [ 0>=1+A ], cost: 1
5.29/2.47	
5.29/2.47	      3: evalspeedpldi2entryin -> evalspeedpldi2returnin : [ 0>=B ], cost: 1
5.29/2.47	
5.29/2.47	      4: evalspeedpldi2bb5in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.29/2.47	
5.29/2.47	      5: evalspeedpldi2bb5in -> evalspeedpldi2returnin : [ 0>=C ], cost: 1
5.29/2.47	
5.29/2.47	      6: evalspeedpldi2bb2in -> evalspeedpldi2bb3in : [ A>=1+B ], cost: 1
5.29/2.47	
5.29/2.47	      7: evalspeedpldi2bb2in -> evalspeedpldi2bb5in : B'=0, [ B>=A ], cost: 1
5.29/2.47	
5.29/2.47	      8: evalspeedpldi2bb3in -> evalspeedpldi2bb5in : B'=1+B, C'=-1+C, [], cost: 1
5.29/2.47	
5.29/2.47	      9: evalspeedpldi2returnin -> evalspeedpldi2stop : [], cost: 1
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Removed unreachable and leaf rules:
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	      0: evalspeedpldi2start -> evalspeedpldi2entryin : [], cost: 1
5.29/2.47	
5.29/2.47	      1: evalspeedpldi2entryin -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 1
5.29/2.47	
5.29/2.47	      4: evalspeedpldi2bb5in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.29/2.47	
5.29/2.47	      6: evalspeedpldi2bb2in -> evalspeedpldi2bb3in : [ A>=1+B ], cost: 1
5.29/2.47	
5.29/2.47	      7: evalspeedpldi2bb2in -> evalspeedpldi2bb5in : B'=0, [ B>=A ], cost: 1
5.29/2.47	
5.29/2.47	      8: evalspeedpldi2bb3in -> evalspeedpldi2bb5in : B'=1+B, C'=-1+C, [], cost: 1
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	### Simplification by acceleration and chaining ###
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Eliminated locations (on linear paths):
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     10: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 2
5.29/2.47	
5.29/2.47	      4: evalspeedpldi2bb5in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.29/2.47	
5.29/2.47	      7: evalspeedpldi2bb2in -> evalspeedpldi2bb5in : B'=0, [ B>=A ], cost: 1
5.29/2.47	
5.29/2.47	     11: evalspeedpldi2bb2in -> evalspeedpldi2bb5in : B'=1+B, C'=-1+C, [ A>=1+B ], cost: 2
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Eliminated locations (on tree-shaped paths):
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     10: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 2
5.29/2.47	
5.29/2.47	     12: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=0, [ C>=1 && B>=A ], cost: 2
5.29/2.47	
5.29/2.47	     13: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=1+B, C'=-1+C, [ C>=1 && A>=1+B ], cost: 3
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Accelerating simple loops of location 2.
5.29/2.47	
5.29/2.47	   Accelerating the following rules:
5.29/2.47	
5.29/2.47	     12: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=0, [ C>=1 && B>=A ], cost: 2
5.29/2.47	
5.29/2.47	     13: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=1+B, C'=-1+C, [ C>=1 && A>=1+B ], cost: 3
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	   Accelerated rule 12 with NONTERM (after strengthening guard), yielding the new rule 14.
5.29/2.47	
5.29/2.47	   Accelerated rule 13 with backward acceleration, yielding the new rule 15.
5.29/2.47	
5.29/2.47	   Accelerated rule 13 with backward acceleration, yielding the new rule 16.
5.29/2.47	
5.29/2.47	   Removing the simple loops: 13.
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Accelerated all simple loops using metering functions (where possible):
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     10: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 2
5.29/2.47	
5.29/2.47	     12: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=0, [ C>=1 && B>=A ], cost: 2
5.29/2.47	
5.29/2.47	     14: evalspeedpldi2bb5in -> [7] : [ C>=1 && B>=A && 0>=A ], cost: INF
5.29/2.47	
5.29/2.47	     15: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=C+B, C'=0, [ C>=1 && A>=1+B && A>=C+B ], cost: 3*C
5.29/2.47	
5.29/2.47	     16: evalspeedpldi2bb5in -> evalspeedpldi2bb5in : B'=A, C'=C-A+B, [ C>=1 && A>=1+B && 1+C-A+B>=1 ], cost: 3*A-3*B
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Chained accelerated rules (with incoming rules):
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     10: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=0, C'=A, [ A>=0 && B>=1 ], cost: 2
5.29/2.47	
5.29/2.47	     17: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=A, C'=0, [ B>=1 && A>=1 && B>=A ], cost: 2+3*A
5.29/2.47	
5.29/2.47	     18: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, C'=A-B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 2+3*B
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Removed unreachable locations (and leaf rules with constant cost):
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     17: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=A, C'=0, [ B>=1 && A>=1 && B>=A ], cost: 2+3*A
5.29/2.47	
5.29/2.47	     18: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, C'=A-B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 2+3*B
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	### Computing asymptotic complexity ###
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Fully simplified ITS problem
5.29/2.47	
5.29/2.47	   Start location: evalspeedpldi2start
5.29/2.47	
5.29/2.47	     17: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=A, C'=0, [ B>=1 && A>=1 && B>=A ], cost: 2+3*A
5.29/2.47	
5.29/2.47	     18: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, C'=A-B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 2+3*B
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Computing asymptotic complexity for rule 17
5.29/2.47	
5.29/2.47	   Simplified the guard:
5.29/2.47	
5.29/2.47	     17: evalspeedpldi2start -> evalspeedpldi2bb5in : A'=B, B'=A, C'=0, [ A>=1 && B>=A ], cost: 2+3*A
5.29/2.47	
5.29/2.47	   Solved the limit problem by the following transformations:
5.29/2.47	
5.29/2.47	      Created initial limit problem:
5.29/2.47	
5.29/2.47	      A (+/+!), 1-A+B (+/+!), 2+3*A (+) [not solved]
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	      removing all constraints (solved by SMT)
5.29/2.47	
5.29/2.47	      resulting limit problem: [solved]
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	      applying transformation rule (C) using substitution {A==n,B==n}
5.29/2.47	
5.29/2.47	      resulting limit problem:
5.29/2.47	
5.29/2.47	      [solved]
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	   Solution:
5.29/2.47	
5.29/2.47	      A / n
5.29/2.47	
5.29/2.47	      B / n
5.29/2.47	
5.29/2.47	   Resulting cost 2+3*n has complexity: Poly(n^1)
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Found new complexity Poly(n^1).
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	Obtained the following overall complexity (w.r.t. the length of the input n):
5.29/2.47	
5.29/2.47	   Complexity:  Poly(n^1)
5.29/2.47	
5.29/2.47	   Cpx degree:  1
5.29/2.47	
5.29/2.47	   Solved cost: 2+3*n
5.29/2.47	
5.29/2.47	   Rule cost:   2+3*A
5.29/2.47	
5.29/2.47	   Rule guard:  [ A>=1 && B>=A ]
5.29/2.47	
5.29/2.47	
5.29/2.47	
5.29/2.47	WORST_CASE(Omega(n^1),?)
5.29/2.47	
5.29/2.47	
5.29/2.47	----------------------------------------
5.29/2.47	
5.29/2.47	(4)
5.29/2.47	BOUNDS(n^1, INF)
5.29/2.49	EOF