3.35/1.61	WORST_CASE(?, O(1))
3.35/1.61	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.35/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.61	
3.35/1.61	
3.35/1.61	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.35/1.61	
3.35/1.61	(0) CpxIntTrs
3.35/1.61	(1) Koat2 Proof [FINISHED, 30 ms]
3.35/1.61	(2) BOUNDS(1, 1)
3.35/1.61	
3.35/1.61	
3.35/1.61	----------------------------------------
3.35/1.61	
3.35/1.61	(0)
3.35/1.61	Obligation:
3.35/1.61	Complexity Int TRS consisting of the following rules:
3.35/1.61	eval_relation1_start(v_x, v_y) -> Com_1(eval_relation1_bb0_in(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_bb0_in(v_x, v_y) -> Com_1(eval_relation1_0(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_0(v_x, v_y) -> Com_1(eval_relation1_1(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_1(v_x, v_y) -> Com_1(eval_relation1_2(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_2(v_x, v_y) -> Com_1(eval_relation1_3(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_3(v_x, v_y) -> Com_1(eval_relation1_4(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_4(v_x, v_y) -> Com_1(eval_relation1_5(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_5(v_x, v_y) -> Com_1(eval_relation1_bb1_in(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_bb1_in(v_x, v_y) -> Com_1(eval_relation1_6(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_6(v_x, v_y) -> Com_1(eval_relation1_7(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_7(v_x, v_y) -> Com_1(eval_relation1_bb2_in(v_x, v_y)) :|: TRUE
3.35/1.61	eval_relation1_bb2_in(v_x, v_y) -> Com_1(eval_relation1_stop(v_x, v_y)) :|: TRUE
3.35/1.61	
3.35/1.61	The start-symbols are:[eval_relation1_start_2]
3.35/1.61	
3.35/1.61	
3.35/1.61	----------------------------------------
3.35/1.61	
3.35/1.61	(1) Koat2 Proof (FINISHED)
3.35/1.61	YES( ?, 12 {O(1)})
3.35/1.61	
3.35/1.61	
3.35/1.61	
3.35/1.61	Initial Complexity Problem:
3.35/1.61	
3.35/1.61	  Start:  evalrelation1start  
3.35/1.61	
3.35/1.61	  Program_Vars:    
3.35/1.61	
3.35/1.61	  Temp_Vars:    
3.35/1.61	
3.35/1.61	  Locations:  evalrelation10, evalrelation11, evalrelation12, evalrelation13, evalrelation14, evalrelation15, evalrelation16, evalrelation17, evalrelation1bb0in, evalrelation1bb1in, evalrelation1bb2in, evalrelation1start, evalrelation1stop  
3.35/1.61	
3.35/1.61	  Transitions:
3.35/1.61	
3.35/1.61	  evalrelation10 -> evalrelation11:|:
3.35/1.61	
3.35/1.61	  evalrelation11 -> evalrelation12:|:
3.35/1.61	
3.35/1.61	  evalrelation12 -> evalrelation13:|:
3.35/1.61	
3.35/1.61	  evalrelation13 -> evalrelation14:|:
3.35/1.61	
3.35/1.61	  evalrelation14 -> evalrelation15:|:
3.35/1.61	
3.35/1.61	  evalrelation15 -> evalrelation1bb1in:|:
3.35/1.61	
3.35/1.61	  evalrelation16 -> evalrelation17:|:
3.35/1.61	
3.35/1.61	  evalrelation17 -> evalrelation1bb2in:|:
3.35/1.61	
3.35/1.61	  evalrelation1bb0in -> evalrelation10:|:
3.35/1.61	
3.35/1.61	  evalrelation1bb1in -> evalrelation16:|:
3.35/1.61	
3.35/1.61	  evalrelation1bb2in -> evalrelation1stop:|:
3.35/1.61	
3.35/1.61	  evalrelation1start -> evalrelation1bb0in:|:  
3.35/1.61	
3.35/1.61	
3.35/1.61	
3.35/1.61	Timebounds: 
3.35/1.61	
3.35/1.61	  Overall timebound: 12 {O(1)}
3.35/1.61	
3.35/1.61	  2: evalrelation10->evalrelation11: 1 {O(1)}
3.35/1.61	
3.35/1.61	  3: evalrelation11->evalrelation12: 1 {O(1)}
3.35/1.61	
3.35/1.61	  4: evalrelation12->evalrelation13: 1 {O(1)}
3.35/1.61	
3.35/1.61	  5: evalrelation13->evalrelation14: 1 {O(1)}
3.35/1.61	
3.35/1.61	  6: evalrelation14->evalrelation15: 1 {O(1)}
3.35/1.61	
3.35/1.61	  7: evalrelation15->evalrelation1bb1in: 1 {O(1)}
3.35/1.61	
3.35/1.61	  9: evalrelation16->evalrelation17: 1 {O(1)}
3.35/1.61	
3.35/1.61	  10: evalrelation17->evalrelation1bb2in: 1 {O(1)}
3.35/1.61	
3.35/1.61	  1: evalrelation1bb0in->evalrelation10: 1 {O(1)}
3.35/1.61	
3.35/1.61	  8: evalrelation1bb1in->evalrelation16: 1 {O(1)}
3.35/1.61	
3.35/1.61	  11: evalrelation1bb2in->evalrelation1stop: 1 {O(1)}
3.35/1.61	
3.35/1.61	  0: evalrelation1start->evalrelation1bb0in: 1 {O(1)}
3.35/1.61	
3.35/1.61	
3.35/1.61	
3.35/1.61	Costbounds:
3.35/1.61	
3.35/1.61	  Overall costbound: 12 {O(1)}
3.35/1.61	
3.35/1.61	  2: evalrelation10->evalrelation11: 1 {O(1)}
3.35/1.61	
3.35/1.61	  3: evalrelation11->evalrelation12: 1 {O(1)}
3.35/1.61	
3.35/1.61	  4: evalrelation12->evalrelation13: 1 {O(1)}
3.35/1.61	
3.35/1.61	  5: evalrelation13->evalrelation14: 1 {O(1)}
3.35/1.61	
3.35/1.61	  6: evalrelation14->evalrelation15: 1 {O(1)}
3.35/1.61	
3.35/1.61	  7: evalrelation15->evalrelation1bb1in: 1 {O(1)}
3.35/1.61	
3.35/1.61	  9: evalrelation16->evalrelation17: 1 {O(1)}
3.35/1.61	
3.35/1.61	  10: evalrelation17->evalrelation1bb2in: 1 {O(1)}
3.35/1.61	
3.35/1.61	  1: evalrelation1bb0in->evalrelation10: 1 {O(1)}
3.35/1.61	
3.35/1.61	  8: evalrelation1bb1in->evalrelation16: 1 {O(1)}
3.35/1.61	
3.35/1.61	  11: evalrelation1bb2in->evalrelation1stop: 1 {O(1)}
3.35/1.61	
3.35/1.61	  0: evalrelation1start->evalrelation1bb0in: 1 {O(1)}
3.35/1.61	
3.35/1.61	
3.35/1.61	
3.35/1.61	Sizebounds:
3.35/1.61	
3.35/1.61	`Lower:
3.35/1.61	
3.35/1.61	  
3.35/1.61	
3.35/1.61	`Upper:
3.35/1.61	
3.35/1.61	  
3.35/1.61	
3.35/1.61	
3.35/1.61	----------------------------------------
3.35/1.61	
3.35/1.61	(2)
3.35/1.61	BOUNDS(1, 1)
3.35/1.65	EOF