4.71/2.51	WORST_CASE(Omega(n^1), O(n^2))
4.71/2.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.71/2.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.71/2.52	
4.71/2.52	
4.71/2.52	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2)).
4.71/2.52	
4.71/2.52	(0) CpxIntTrs
4.71/2.52	(1) Koat2 Proof [FINISHED, 829 ms]
4.71/2.52	(2) BOUNDS(1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2))
4.71/2.52	(3) Loat Proof [FINISHED, 325 ms]
4.71/2.52	(4) BOUNDS(n^1, INF)
4.71/2.52	
4.71/2.52	
4.71/2.52	----------------------------------------
4.71/2.52	
4.71/2.52	(0)
4.71/2.52	Obligation:
4.71/2.52	Complexity Int TRS consisting of the following rules:
4.71/2.52	evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE
4.71/2.52	evalfentryin(A, B, C) -> Com_1(evalfbb4in(B, A, C)) :|: TRUE
4.71/2.52	evalfbb4in(A, B, C) -> Com_1(evalfbb2in(A, B, A)) :|: B >= 1
4.71/2.52	evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: 0 >= B
4.71/2.52	evalfbb2in(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: C >= A
4.71/2.52	evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C)) :|: A >= C + 1
4.71/2.52	evalfbb1in(A, B, C) -> Com_1(evalfbb2in(A, B, C - 1)) :|: TRUE
4.71/2.52	evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A, B - 1, C)) :|: TRUE
4.71/2.52	evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE
4.71/2.52	
4.71/2.52	The start-symbols are:[evalfstart_3]
4.71/2.52	
4.71/2.52	
4.71/2.52	----------------------------------------
4.71/2.52	
4.71/2.52	(1) Koat2 Proof (FINISHED)
4.71/2.52	YES( ?, 4+2*max([0, Arg_0])+max([0, 1+Arg_0])+max([0, Arg_0*(1+Arg_0)])+max([0, 1+Arg_0]) {O(n^2)})
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Initial Complexity Problem:
4.71/2.52	
4.71/2.52	  Start:  evalfstart  
4.71/2.52	
4.71/2.52	  Program_Vars:  Arg_0, Arg_1, Arg_2  
4.71/2.52	
4.71/2.52	  Temp_Vars:    
4.71/2.52	
4.71/2.52	  Locations:  evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop  
4.71/2.52	
4.71/2.52	  Transitions:
4.71/2.52	
4.71/2.52	  evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|:Arg_2 <= Arg_0 && Arg_0 <= Arg_2 && 1 <= Arg_1
4.71/2.52	
4.71/2.52	  evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_0 && 1 <= Arg_1 && Arg_0 <= Arg_2
4.71/2.52	
4.71/2.52	  evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_0 && 1 <= Arg_1 && Arg_2+1 <= Arg_0
4.71/2.52	
4.71/2.52	  evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2 <= Arg_0 && 1 <= Arg_1
4.71/2.52	
4.71/2.52	  evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1 <= Arg_1
4.71/2.52	
4.71/2.52	  evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0
4.71/2.52	
4.71/2.52	  evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2):|:
4.71/2.52	
4.71/2.52	  evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0
4.71/2.52	
4.71/2.52	  evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2):|:  
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Timebounds: 
4.71/2.52	
4.71/2.52	  Overall timebound: 4+2*max([0, Arg_0])+max([0, 1+Arg_0])+max([0, Arg_0*(1+Arg_0)])+max([0, 1+Arg_0]) {O(n^2)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in: max([0, Arg_0*(1+Arg_0)]) {O(n^2)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in: max([0, 1+Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in: max([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in: max([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in: max([0, 1+Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin: 1 {O(1)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in: 1 {O(1)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop: 1 {O(1)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin: 1 {O(1)}
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Costbounds:
4.71/2.52	
4.71/2.52	  Overall costbound: 4+2*max([0, Arg_0])+max([0, 1+Arg_0])+max([0, Arg_0*(1+Arg_0)])+max([0, 1+Arg_0]) {O(n^2)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in: max([0, Arg_0*(1+Arg_0)]) {O(n^2)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in: max([0, 1+Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in: max([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in: max([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in: max([0, 1+Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin: 1 {O(1)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in: 1 {O(1)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop: 1 {O(1)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin: 1 {O(1)}
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Sizebounds:
4.71/2.52	
4.71/2.52	`Lower:
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_1: 1 {O(1)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_1: 1 {O(1)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_2: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_1: 1 {O(1)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_1: 0 {O(1)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_1: 1 {O(1)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_2: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_1: min([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_2: min([Arg_2, -(1-Arg_1)]) {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_2: Arg_2 {O(n)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_1: min([0, Arg_0]) {O(n)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_2: min([Arg_2, -(1-Arg_1)]) {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}
4.71/2.52	
4.71/2.52	`Upper:
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  6: evalfbb1in->evalfbb2in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  4: evalfbb2in->evalfbb1in, Arg_2: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  5: evalfbb2in->evalfbb3in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  7: evalfbb3in->evalfbb4in, Arg_2: -1+Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  2: evalfbb4in->evalfbb2in, Arg_2: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_1: 0 {O(1)}
4.71/2.52	
4.71/2.52	  3: evalfbb4in->evalfreturnin, Arg_2: max([Arg_2, -1+Arg_1]) {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_1: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  1: evalfentryin->evalfbb4in, Arg_2: Arg_2 {O(n)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_0: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_1: 0 {O(1)}
4.71/2.52	
4.71/2.52	  8: evalfreturnin->evalfstop, Arg_2: max([Arg_2, -1+Arg_1]) {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}
4.71/2.52	
4.71/2.52	  0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}
4.71/2.52	
4.71/2.52	
4.71/2.52	----------------------------------------
4.71/2.52	
4.71/2.52	(2)
4.71/2.52	BOUNDS(1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2))
4.71/2.52	
4.71/2.52	----------------------------------------
4.71/2.52	
4.71/2.52	(3) Loat Proof (FINISHED)
4.71/2.52	
4.71/2.52	
4.71/2.52	### Pre-processing the ITS problem ###
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Initial linear ITS problem
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      0: evalfstart -> evalfentryin : [], cost: 1
4.71/2.52	
4.71/2.52	      1: evalfentryin -> evalfbb4in : A'=B, B'=A, [], cost: 1
4.71/2.52	
4.71/2.52	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=1 ], cost: 1
4.71/2.52	
4.71/2.52	      3: evalfbb4in -> evalfreturnin : [ 0>=B ], cost: 1
4.71/2.52	
4.71/2.52	      4: evalfbb2in -> evalfbb1in : [ C>=A ], cost: 1
4.71/2.52	
4.71/2.52	      5: evalfbb2in -> evalfbb3in : [ A>=1+C ], cost: 1
4.71/2.52	
4.71/2.52	      6: evalfbb1in -> evalfbb2in : C'=-1+C, [], cost: 1
4.71/2.52	
4.71/2.52	      7: evalfbb3in -> evalfbb4in : B'=-1+B, [], cost: 1
4.71/2.52	
4.71/2.52	      8: evalfreturnin -> evalfstop : [], cost: 1
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Removed unreachable and leaf rules:
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      0: evalfstart -> evalfentryin : [], cost: 1
4.71/2.52	
4.71/2.52	      1: evalfentryin -> evalfbb4in : A'=B, B'=A, [], cost: 1
4.71/2.52	
4.71/2.52	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=1 ], cost: 1
4.71/2.52	
4.71/2.52	      4: evalfbb2in -> evalfbb1in : [ C>=A ], cost: 1
4.71/2.52	
4.71/2.52	      5: evalfbb2in -> evalfbb3in : [ A>=1+C ], cost: 1
4.71/2.52	
4.71/2.52	      6: evalfbb1in -> evalfbb2in : C'=-1+C, [], cost: 1
4.71/2.52	
4.71/2.52	      7: evalfbb3in -> evalfbb4in : B'=-1+B, [], cost: 1
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	### Simplification by acceleration and chaining ###
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Eliminated locations (on linear paths):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=1 ], cost: 1
4.71/2.52	
4.71/2.52	     10: evalfbb2in -> evalfbb2in : C'=-1+C, [ C>=A ], cost: 2
4.71/2.52	
4.71/2.52	     11: evalfbb2in -> evalfbb4in : B'=-1+B, [ A>=1+C ], cost: 2
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Accelerating simple loops of location 3.
4.71/2.52	
4.71/2.52	   Accelerating the following rules:
4.71/2.52	
4.71/2.52	     10: evalfbb2in -> evalfbb2in : C'=-1+C, [ C>=A ], cost: 2
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	   Accelerated rule 10 with metering function 1+C-A, yielding the new rule 12.
4.71/2.52	
4.71/2.52	   Removing the simple loops: 10.
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Accelerated all simple loops using metering functions (where possible):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=1 ], cost: 1
4.71/2.52	
4.71/2.52	     11: evalfbb2in -> evalfbb4in : B'=-1+B, [ A>=1+C ], cost: 2
4.71/2.52	
4.71/2.52	     12: evalfbb2in -> evalfbb2in : C'=-1+A, [ C>=A ], cost: 2+2*C-2*A
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Chained accelerated rules (with incoming rules):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=1 ], cost: 1
4.71/2.52	
4.71/2.52	     13: evalfbb4in -> evalfbb2in : C'=-1+A, [ B>=1 ], cost: 3
4.71/2.52	
4.71/2.52	     11: evalfbb2in -> evalfbb4in : B'=-1+B, [ A>=1+C ], cost: 2
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Eliminated locations (on tree-shaped paths):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	     14: evalfbb4in -> evalfbb4in : B'=-1+B, C'=-1+A, [ B>=1 ], cost: 5
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Accelerating simple loops of location 2.
4.71/2.52	
4.71/2.52	   Accelerating the following rules:
4.71/2.52	
4.71/2.52	     14: evalfbb4in -> evalfbb4in : B'=-1+B, C'=-1+A, [ B>=1 ], cost: 5
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	   Accelerated rule 14 with metering function B, yielding the new rule 15.
4.71/2.52	
4.71/2.52	   Removing the simple loops: 14.
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Accelerated all simple loops using metering functions (where possible):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	     15: evalfbb4in -> evalfbb4in : B'=0, C'=-1+A, [ B>=1 ], cost: 5*B
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Chained accelerated rules (with incoming rules):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	      9: evalfstart -> evalfbb4in : A'=B, B'=A, [], cost: 2
4.71/2.52	
4.71/2.52	     16: evalfstart -> evalfbb4in : A'=B, B'=0, C'=-1+B, [ A>=1 ], cost: 2+5*A
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Removed unreachable locations (and leaf rules with constant cost):
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	     16: evalfstart -> evalfbb4in : A'=B, B'=0, C'=-1+B, [ A>=1 ], cost: 2+5*A
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	### Computing asymptotic complexity ###
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Fully simplified ITS problem
4.71/2.52	
4.71/2.52	   Start location: evalfstart
4.71/2.52	
4.71/2.52	     16: evalfstart -> evalfbb4in : A'=B, B'=0, C'=-1+B, [ A>=1 ], cost: 2+5*A
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Computing asymptotic complexity for rule 16
4.71/2.52	
4.71/2.52	   Solved the limit problem by the following transformations:
4.71/2.52	
4.71/2.52	      Created initial limit problem:
4.71/2.52	
4.71/2.52	      2+5*A (+), A (+/+!) [not solved]
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	      removing all constraints (solved by SMT)
4.71/2.52	
4.71/2.52	      resulting limit problem: [solved]
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	      applying transformation rule (C) using substitution {A==n}
4.71/2.52	
4.71/2.52	      resulting limit problem:
4.71/2.52	
4.71/2.52	      [solved]
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	   Solution:
4.71/2.52	
4.71/2.52	      A / n
4.71/2.52	
4.71/2.52	   Resulting cost 2+5*n has complexity: Poly(n^1)
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Found new complexity Poly(n^1).
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	Obtained the following overall complexity (w.r.t. the length of the input n):
4.71/2.52	
4.71/2.52	   Complexity:  Poly(n^1)
4.71/2.52	
4.71/2.52	   Cpx degree:  1
4.71/2.52	
4.71/2.52	   Solved cost: 2+5*n
4.71/2.52	
4.71/2.52	   Rule cost:   2+5*A
4.71/2.52	
4.71/2.52	   Rule guard:  [ A>=1 ]
4.71/2.52	
4.71/2.52	
4.71/2.52	
4.71/2.52	WORST_CASE(Omega(n^1),?)
4.71/2.52	
4.71/2.52	
4.71/2.52	----------------------------------------
4.71/2.52	
4.71/2.52	(4)
4.71/2.52	BOUNDS(n^1, INF)
4.71/2.53	EOF