5.47/2.46	MAYBE
5.47/2.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.47/2.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.47/2.47	
5.47/2.47	
5.47/2.47	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
5.47/2.47	
5.47/2.47	(0) CpxIntTrs
5.47/2.47	(1) Loat Proof [FINISHED, 421 ms]
5.47/2.47	(2) BOUNDS(1, INF)
5.47/2.47	
5.47/2.47	
5.47/2.47	----------------------------------------
5.47/2.47	
5.47/2.47	(0)
5.47/2.47	Obligation:
5.47/2.47	Complexity Int TRS consisting of the following rules:
5.47/2.47	eval_start_start(v__0, v__01, v_x, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_bb0_in(v__0, v__01, v_x, v_y) -> Com_1(eval_start_0(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_0(v__0, v__01, v_x, v_y) -> Com_1(eval_start_1(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_1(v__0, v__01, v_x, v_y) -> Com_1(eval_start_2(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_2(v__0, v__01, v_x, v_y) -> Com_1(eval_start_3(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_3(v__0, v__01, v_x, v_y) -> Com_1(eval_start_4(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_4(v__0, v__01, v_x, v_y) -> Com_1(eval_start_5(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_5(v__0, v__01, v_x, v_y) -> Com_1(eval_start_6(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_6(v__0, v__01, v_x, v_y) -> Com_1(eval_start_7(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_7(v__0, v__01, v_x, v_y) -> Com_1(eval_start_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v_x, v_y)) :|: v__0 > 0
5.47/2.47	eval_start_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v_x, v_y)) :|: v__0 <= 0
5.47/2.47	eval_start_bb2_in(v__0, v__01, v_x, v_y) -> Com_1(eval_start_bb1_in(v__01, v__0 - 1, v_x, v_y)) :|: TRUE
5.47/2.47	eval_start_bb3_in(v__0, v__01, v_x, v_y) -> Com_1(eval_start_stop(v__0, v__01, v_x, v_y)) :|: TRUE
5.47/2.47	
5.47/2.47	The start-symbols are:[eval_start_start_4]
5.47/2.47	
5.47/2.47	
5.47/2.47	----------------------------------------
5.47/2.47	
5.47/2.47	(1) Loat Proof (FINISHED)
5.47/2.47	
5.47/2.47	
5.47/2.47	### Pre-processing the ITS problem ###
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Initial linear ITS problem
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.47/2.47	
5.47/2.47	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.47/2.47	
5.47/2.47	      2: evalstart0 -> evalstart1 : [], cost: 1
5.47/2.47	
5.47/2.47	      3: evalstart1 -> evalstart2 : [], cost: 1
5.47/2.47	
5.47/2.47	      4: evalstart2 -> evalstart3 : [], cost: 1
5.47/2.47	
5.47/2.47	      5: evalstart3 -> evalstart4 : [], cost: 1
5.47/2.47	
5.47/2.47	      6: evalstart4 -> evalstart5 : [], cost: 1
5.47/2.47	
5.47/2.47	      7: evalstart5 -> evalstart6 : [], cost: 1
5.47/2.47	
5.47/2.47	      8: evalstart6 -> evalstart7 : [], cost: 1
5.47/2.47	
5.47/2.47	      9: evalstart7 -> evalstartbb1in : A'=B, C'=D, [], cost: 1
5.47/2.47	
5.47/2.47	     10: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1
5.47/2.47	
5.47/2.47	     11: evalstartbb1in -> evalstartbb3in : [ 0>=A ], cost: 1
5.47/2.47	
5.47/2.47	     12: evalstartbb2in -> evalstartbb1in : A'=C, C'=-1+A, [], cost: 1
5.47/2.47	
5.47/2.47	     13: evalstartbb3in -> evalstartstop : [], cost: 1
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Removed unreachable and leaf rules:
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.47/2.47	
5.47/2.47	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.47/2.47	
5.47/2.47	      2: evalstart0 -> evalstart1 : [], cost: 1
5.47/2.47	
5.47/2.47	      3: evalstart1 -> evalstart2 : [], cost: 1
5.47/2.47	
5.47/2.47	      4: evalstart2 -> evalstart3 : [], cost: 1
5.47/2.47	
5.47/2.47	      5: evalstart3 -> evalstart4 : [], cost: 1
5.47/2.47	
5.47/2.47	      6: evalstart4 -> evalstart5 : [], cost: 1
5.47/2.47	
5.47/2.47	      7: evalstart5 -> evalstart6 : [], cost: 1
5.47/2.47	
5.47/2.47	      8: evalstart6 -> evalstart7 : [], cost: 1
5.47/2.47	
5.47/2.47	      9: evalstart7 -> evalstartbb1in : A'=B, C'=D, [], cost: 1
5.47/2.47	
5.47/2.47	     10: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1
5.47/2.47	
5.47/2.47	     12: evalstartbb2in -> evalstartbb1in : A'=C, C'=-1+A, [], cost: 1
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	### Simplification by acceleration and chaining ###
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Eliminated locations (on linear paths):
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	     22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 10
5.47/2.47	
5.47/2.47	     23: evalstartbb1in -> evalstartbb1in : A'=C, C'=-1+A, [ A>=1 ], cost: 2
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Accelerating simple loops of location 10.
5.47/2.47	
5.47/2.47	   Accelerating the following rules:
5.47/2.47	
5.47/2.47	     23: evalstartbb1in -> evalstartbb1in : A'=C, C'=-1+A, [ A>=1 ], cost: 2
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	   Found no metering function for rule 23.
5.47/2.47	
5.47/2.47	   Removing the simple loops:.
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Accelerated all simple loops using metering functions (where possible):
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	     22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 10
5.47/2.47	
5.47/2.47	     23: evalstartbb1in -> evalstartbb1in : A'=C, C'=-1+A, [ A>=1 ], cost: 2
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Chained accelerated rules (with incoming rules):
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	     22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 10
5.47/2.47	
5.47/2.47	     24: evalstartstart -> evalstartbb1in : A'=D, C'=-1+B, [ B>=1 ], cost: 12
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Removed unreachable locations (and leaf rules with constant cost):
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	### Computing asymptotic complexity ###
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Fully simplified ITS problem
5.47/2.47	
5.47/2.47	   Start location: evalstartstart
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	Obtained the following overall complexity (w.r.t. the length of the input n):
5.47/2.47	
5.47/2.47	   Complexity:  Unknown
5.47/2.47	
5.47/2.47	   Cpx degree:  ?
5.47/2.47	
5.47/2.47	   Solved cost: 0
5.47/2.47	
5.47/2.47	   Rule cost:   0
5.47/2.47	
5.47/2.47	   Rule guard:  []
5.47/2.47	
5.47/2.47	
5.47/2.47	
5.47/2.47	WORST_CASE(Omega(0),?)
5.47/2.47	
5.47/2.47	
5.47/2.47	----------------------------------------
5.47/2.47	
5.47/2.47	(2)
5.47/2.47	BOUNDS(1, INF)
5.47/2.50	EOF