12.74/9.47	WORST_CASE(Omega(n^1), O(n^2))
12.74/9.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
12.74/9.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.74/9.48	
12.74/9.48	
12.74/9.48	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(10 + 2 * Arg_2, 10) + nat(Arg_2^2) + nat(4 * Arg_2) + max(2, 2 + Arg_2) + nat(1 + 4 * Arg_2) + nat(Arg_2^2) * nat(Arg_2) + nat(Arg_2)^2).
12.74/9.48	
12.74/9.48	(0) CpxIntTrs
12.74/9.48	(1) Loat Proof [FINISHED, 1117 ms]
12.74/9.48	(2) BOUNDS(n^1, INF)
12.74/9.48	
12.74/9.48	
12.74/9.48	----------------------------------------
12.74/9.48	
12.74/9.48	(0)
12.74/9.48	Obligation:
12.74/9.48	Complexity Int TRS consisting of the following rules:
12.74/9.48	eval_foo_start(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb0_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_bb0_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_0(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_0(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_1(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_1(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_2(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_2(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_3(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_3(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_4(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_4(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_5(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_5(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_6(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_6(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_7(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_7(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, 0, v_n)) :|: TRUE
12.74/9.48	eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb2_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_x_0 > 0
12.74/9.48	eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb5_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_x_0 <= 0
12.74/9.48	eval_foo_bb2_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_10(v_x_0 - 1, v_r_0 + 1, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_10(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_11(v_1, v_2, nondef_0, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_11(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_2, v_r_0, v_x_0)) :|: v_3 > 0
12.74/9.48	eval_foo_11(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_2, v_1)) :|: v_3 <= 0
12.74/9.48	eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb4_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_p_0 > 0
12.74/9.48	eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, 0, v_1)) :|: v_p_0 <= 0
12.74/9.48	eval_foo_bb4_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0 - 1, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	eval_foo_bb5_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_stop(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE
12.74/9.48	
12.74/9.48	The start-symbols are:[eval_foo_start_7]
12.74/9.48	
12.74/9.48	
12.74/9.48	----------------------------------------
12.74/9.48	
12.74/9.48	(1) Loat Proof (FINISHED)
12.74/9.48	
12.74/9.48	
12.74/9.48	### Pre-processing the ITS problem ###
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Initial linear ITS problem
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	      0: evalfoostart -> evalfoobb0in : [], cost: 1
12.74/9.48	
12.74/9.48	      1: evalfoobb0in -> evalfoo0 : [], cost: 1
12.74/9.48	
12.74/9.48	      2: evalfoo0 -> evalfoo1 : [], cost: 1
12.74/9.48	
12.74/9.48	      3: evalfoo1 -> evalfoo2 : [], cost: 1
12.74/9.48	
12.74/9.48	      4: evalfoo2 -> evalfoo3 : [], cost: 1
12.74/9.48	
12.74/9.48	      5: evalfoo3 -> evalfoo4 : [], cost: 1
12.74/9.48	
12.74/9.48	      6: evalfoo4 -> evalfoo5 : [], cost: 1
12.74/9.48	
12.74/9.48	      7: evalfoo5 -> evalfoo6 : [], cost: 1
12.74/9.48	
12.74/9.48	      8: evalfoo6 -> evalfoo7 : [], cost: 1
12.74/9.48	
12.74/9.48	      9: evalfoo7 -> evalfoobb1in : A'=0, B'=C, [], cost: 1
12.74/9.48	
12.74/9.48	     10: evalfoobb1in -> evalfoobb2in : [ B>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     11: evalfoobb1in -> evalfoobb5in : [ 0>=B ], cost: 1
12.74/9.48	
12.74/9.48	     12: evalfoobb2in -> evalfoo10 : D'=-1+B, E'=1+A, [], cost: 1
12.74/9.48	
12.74/9.48	     13: evalfoo10 -> evalfoo11 : F'=free, [], cost: 1
12.74/9.48	
12.74/9.48	     14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1
12.74/9.48	
12.74/9.48	     16: evalfoobb3in -> evalfoobb4in : [ G>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	     18: evalfoobb4in -> evalfoobb3in : G'=-1+G, [], cost: 1
12.74/9.48	
12.74/9.48	     19: evalfoobb5in -> evalfoostop : [], cost: 1
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Removed unreachable and leaf rules:
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	      0: evalfoostart -> evalfoobb0in : [], cost: 1
12.74/9.48	
12.74/9.48	      1: evalfoobb0in -> evalfoo0 : [], cost: 1
12.74/9.48	
12.74/9.48	      2: evalfoo0 -> evalfoo1 : [], cost: 1
12.74/9.48	
12.74/9.48	      3: evalfoo1 -> evalfoo2 : [], cost: 1
12.74/9.48	
12.74/9.48	      4: evalfoo2 -> evalfoo3 : [], cost: 1
12.74/9.48	
12.74/9.48	      5: evalfoo3 -> evalfoo4 : [], cost: 1
12.74/9.48	
12.74/9.48	      6: evalfoo4 -> evalfoo5 : [], cost: 1
12.74/9.48	
12.74/9.48	      7: evalfoo5 -> evalfoo6 : [], cost: 1
12.74/9.48	
12.74/9.48	      8: evalfoo6 -> evalfoo7 : [], cost: 1
12.74/9.48	
12.74/9.48	      9: evalfoo7 -> evalfoobb1in : A'=0, B'=C, [], cost: 1
12.74/9.48	
12.74/9.48	     10: evalfoobb1in -> evalfoobb2in : [ B>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     12: evalfoobb2in -> evalfoo10 : D'=-1+B, E'=1+A, [], cost: 1
12.74/9.48	
12.74/9.48	     13: evalfoo10 -> evalfoo11 : F'=free, [], cost: 1
12.74/9.48	
12.74/9.48	     14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1
12.74/9.48	
12.74/9.48	     16: evalfoobb3in -> evalfoobb4in : [ G>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	     18: evalfoobb4in -> evalfoobb3in : G'=-1+G, [], cost: 1
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	### Simplification by acceleration and chaining ###
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Eliminated locations (on linear paths):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     30: evalfoobb1in -> evalfoo11 : D'=-1+B, E'=1+A, F'=free, [ B>=1 ], cost: 3
12.74/9.48	
12.74/9.48	     14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	     31: evalfoobb3in -> evalfoobb3in : G'=-1+G, [ G>=1 ], cost: 2
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerating simple loops of location 14.
12.74/9.48	
12.74/9.48	   Accelerating the following rules:
12.74/9.48	
12.74/9.48	     31: evalfoobb3in -> evalfoobb3in : G'=-1+G, [ G>=1 ], cost: 2
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	   Accelerated rule 31 with metering function G, yielding the new rule 32.
12.74/9.48	
12.74/9.48	   Removing the simple loops: 31.
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerated all simple loops using metering functions (where possible):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     30: evalfoobb1in -> evalfoo11 : D'=-1+B, E'=1+A, F'=free, [ B>=1 ], cost: 3
12.74/9.48	
12.74/9.48	     14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	     32: evalfoobb3in -> evalfoobb3in : G'=0, [ G>=1 ], cost: 2*G
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Chained accelerated rules (with incoming rules):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     30: evalfoobb1in -> evalfoo11 : D'=-1+B, E'=1+A, F'=free, [ B>=1 ], cost: 3
12.74/9.48	
12.74/9.48	     14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1
12.74/9.48	
12.74/9.48	     15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1
12.74/9.48	
12.74/9.48	     33: evalfoo11 -> evalfoobb3in : G'=0, [ F>=1 && E>=1 ], cost: 1+2*E
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Eliminated locations (on tree-shaped paths):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     34: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 ], cost: 4
12.74/9.48	
12.74/9.48	     35: evalfoobb1in -> evalfoobb1in : A'=1+A, B'=-1+B, D'=-1+B, E'=1+A, F'=free, [ B>=1 && 0>=free ], cost: 4
12.74/9.48	
12.74/9.48	     36: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerating simple loops of location 10.
12.74/9.48	
12.74/9.48	   Accelerating the following rules:
12.74/9.48	
12.74/9.48	     35: evalfoobb1in -> evalfoobb1in : A'=1+A, B'=-1+B, D'=-1+B, E'=1+A, F'=free, [ B>=1 && 0>=free ], cost: 4
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	   Accelerated rule 35 with metering function B, yielding the new rule 37.
12.74/9.48	
12.74/9.48	   Removing the simple loops: 35.
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerated all simple loops using metering functions (where possible):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     34: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 ], cost: 4
12.74/9.48	
12.74/9.48	     36: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	     37: evalfoobb1in -> evalfoobb1in : A'=A+B, B'=0, D'=0, E'=A+B, F'=free, [ B>=1 && 0>=free ], cost: 4*B
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Chained accelerated rules (with incoming rules):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     39: evalfoostart -> evalfoobb1in : A'=C, B'=0, D'=0, E'=C, F'=free, [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     34: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 ], cost: 4
12.74/9.48	
12.74/9.48	     36: evalfoobb1in -> evalfoobb3in : D'=-1+B, E'=1+A, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	     17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1
12.74/9.48	
12.74/9.48	     38: evalfoobb3in -> evalfoobb1in : A'=D, B'=0, D'=0, E'=D, F'=free, [ 0>=G && D>=1 && 0>=free ], cost: 1+4*D
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Eliminated locations (on tree-shaped paths):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     39: evalfoostart -> evalfoobb1in : A'=C, B'=0, D'=0, E'=C, F'=free, [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     40: evalfoobb1in -> evalfoobb1in : A'=0, B'=-1+B, D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 && 0>=1+A ], cost: 5
12.74/9.48	
12.74/9.48	     41: evalfoobb1in -> evalfoobb1in : A'=0, B'=-1+B, D'=-1+B, E'=1+A, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 7+2*A
12.74/9.48	
12.74/9.48	     42: evalfoobb1in -> [20] : [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerating simple loops of location 10.
12.74/9.48	
12.74/9.48	   Accelerating the following rules:
12.74/9.48	
12.74/9.48	     40: evalfoobb1in -> evalfoobb1in : A'=0, B'=-1+B, D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 && 0>=1+A ], cost: 5
12.74/9.48	
12.74/9.48	     41: evalfoobb1in -> evalfoobb1in : A'=0, B'=-1+B, D'=-1+B, E'=1+A, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 7+2*A
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	   Found no metering function for rule 40.
12.74/9.48	
12.74/9.48	   Accelerated rule 41 with metering function B, yielding the new rule 43.
12.74/9.48	
12.74/9.48	   Removing the simple loops: 41.
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Accelerated all simple loops using metering functions (where possible):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     39: evalfoostart -> evalfoobb1in : A'=C, B'=0, D'=0, E'=C, F'=free, [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     40: evalfoobb1in -> evalfoobb1in : A'=0, B'=-1+B, D'=-1+B, E'=1+A, F'=free, G'=1+A, [ B>=1 && free>=1 && 0>=1+A ], cost: 5
12.74/9.48	
12.74/9.48	     42: evalfoobb1in -> [20] : [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	     43: evalfoobb1in -> evalfoobb1in : A'=0, B'=0, D'=0, E'=1, F'=free, G'=0, [ B>=1 && free>=1 && 1+A>=1 ], cost: 7*B
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Chained accelerated rules (with incoming rules):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     28: evalfoostart -> evalfoobb1in : A'=0, B'=C, [], cost: 10
12.74/9.48	
12.74/9.48	     39: evalfoostart -> evalfoobb1in : A'=C, B'=0, D'=0, E'=C, F'=free, [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     44: evalfoostart -> evalfoobb1in : A'=0, B'=0, D'=0, E'=1, F'=free, G'=0, [ C>=1 && free>=1 ], cost: 10+7*C
12.74/9.48	
12.74/9.48	     42: evalfoobb1in -> [20] : [ B>=1 && free>=1 && 1+A>=1 ], cost: 6+2*A
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Eliminated locations (on tree-shaped paths):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     45: evalfoostart -> [20] : A'=0, B'=C, [ C>=1 && free>=1 ], cost: 16
12.74/9.48	
12.74/9.48	     46: evalfoostart -> [22] : [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     47: evalfoostart -> [22] : [ C>=1 && free>=1 ], cost: 10+7*C
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Applied pruning (of leafs and parallel rules):
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     46: evalfoostart -> [22] : [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     47: evalfoostart -> [22] : [ C>=1 && free>=1 ], cost: 10+7*C
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	### Computing asymptotic complexity ###
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Fully simplified ITS problem
12.74/9.48	
12.74/9.48	   Start location: evalfoostart
12.74/9.48	
12.74/9.48	     46: evalfoostart -> [22] : [ C>=1 && 0>=free ], cost: 10+4*C
12.74/9.48	
12.74/9.48	     47: evalfoostart -> [22] : [ C>=1 && free>=1 ], cost: 10+7*C
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Computing asymptotic complexity for rule 46
12.74/9.48	
12.74/9.48	   Solved the limit problem by the following transformations:
12.74/9.48	
12.74/9.48	      Created initial limit problem:
12.74/9.48	
12.74/9.48	      1-free (+/+!), C (+/+!), 10+4*C (+) [not solved]
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	      removing all constraints (solved by SMT)
12.74/9.48	
12.74/9.48	      resulting limit problem: [solved]
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	      applying transformation rule (C) using substitution {free==0,C==n}
12.74/9.48	
12.74/9.48	      resulting limit problem:
12.74/9.48	
12.74/9.48	      [solved]
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	   Solution:
12.74/9.48	
12.74/9.48	      free / 0
12.74/9.48	
12.74/9.48	      C / n
12.74/9.48	
12.74/9.48	   Resulting cost 10+4*n has complexity: Poly(n^1)
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Found new complexity Poly(n^1).
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	Obtained the following overall complexity (w.r.t. the length of the input n):
12.74/9.48	
12.74/9.48	   Complexity:  Poly(n^1)
12.74/9.48	
12.74/9.48	   Cpx degree:  1
12.74/9.48	
12.74/9.48	   Solved cost: 10+4*n
12.74/9.48	
12.74/9.48	   Rule cost:   10+4*C
12.74/9.48	
12.74/9.48	   Rule guard:  [ C>=1 && 0>=free ]
12.74/9.48	
12.74/9.48	
12.74/9.48	
12.74/9.48	WORST_CASE(Omega(n^1),?)
12.74/9.48	
12.74/9.48	
12.74/9.48	----------------------------------------
12.74/9.48	
12.74/9.48	(2)
12.74/9.48	BOUNDS(n^1, INF)
12.90/9.50	EOF