6.79/3.14	MAYBE
6.79/3.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.79/3.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.79/3.15	
6.79/3.15	
6.79/3.15	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.79/3.15	
6.79/3.15	(0) CpxIntTrs
6.79/3.15	(1) Loat Proof [FINISHED, 629 ms]
6.79/3.15	(2) BOUNDS(1, INF)
6.79/3.15	
6.79/3.15	
6.79/3.15	----------------------------------------
6.79/3.15	
6.79/3.15	(0)
6.79/3.15	Obligation:
6.79/3.15	Complexity Int TRS consisting of the following rules:
6.79/3.15	eval_speedFails4_start(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb0_in(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_bb0_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_1(v__, v__0, nondef_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_1(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_2(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_2(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_3(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_3(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_4(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_4(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_5(1, v__0, v_0, v_n, v_x)) :|: v_0 >= 1
6.79/3.15	eval_speedFails4_4(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_5(-(1), v__0, v_0, v_n, v_x)) :|: v_0 < 1
6.79/3.15	eval_speedFails4_5(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_6(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_6(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_7(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_7(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb1_in(v__, v_x, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	eval_speedFails4_bb1_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb2_in(v__, v__0, v_0, v_n, v_x)) :|: v__0 <= v_n
6.79/3.15	eval_speedFails4_bb1_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb3_in(v__, v__0, v_0, v_n, v_x)) :|: v__0 > v_n
6.79/3.15	eval_speedFails4_bb2_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb1_in(v__, v__0 + v__, v_0, v_n, v_x)) :|: v_0 >= 1
6.79/3.15	eval_speedFails4_bb2_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_bb1_in(v__, v__0 - v__, v_0, v_n, v_x)) :|: v_0 < 1
6.79/3.15	eval_speedFails4_bb3_in(v__, v__0, v_0, v_n, v_x) -> Com_1(eval_speedFails4_stop(v__, v__0, v_0, v_n, v_x)) :|: TRUE
6.79/3.15	
6.79/3.15	The start-symbols are:[eval_speedFails4_start_5]
6.79/3.15	
6.79/3.15	
6.79/3.15	----------------------------------------
6.79/3.15	
6.79/3.15	(1) Loat Proof (FINISHED)
6.79/3.15	
6.79/3.15	
6.79/3.15	### Pre-processing the ITS problem ###
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Initial linear ITS problem
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	      0: evalspeedFails4start -> evalspeedFails4bb0in : [], cost: 1
6.79/3.15	
6.79/3.15	      1: evalspeedFails4bb0in -> evalspeedFails41 : A'=free, [], cost: 1
6.79/3.15	
6.79/3.15	      2: evalspeedFails41 -> evalspeedFails42 : [], cost: 1
6.79/3.15	
6.79/3.15	      3: evalspeedFails42 -> evalspeedFails43 : [], cost: 1
6.79/3.15	
6.79/3.15	      4: evalspeedFails43 -> evalspeedFails44 : [], cost: 1
6.79/3.15	
6.79/3.15	      5: evalspeedFails44 -> evalspeedFails45 : B'=1, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	      6: evalspeedFails44 -> evalspeedFails45 : B'=-1, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	      7: evalspeedFails45 -> evalspeedFails46 : [], cost: 1
6.79/3.15	
6.79/3.15	      8: evalspeedFails46 -> evalspeedFails47 : [], cost: 1
6.79/3.15	
6.79/3.15	      9: evalspeedFails47 -> evalspeedFails4bb1in : C'=D, [], cost: 1
6.79/3.15	
6.79/3.15	     10: evalspeedFails4bb1in -> evalspeedFails4bb2in : [ E>=C ], cost: 1
6.79/3.15	
6.79/3.15	     11: evalspeedFails4bb1in -> evalspeedFails4bb3in : [ C>=1+E ], cost: 1
6.79/3.15	
6.79/3.15	     12: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C+B, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	     13: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C-B, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	     14: evalspeedFails4bb3in -> evalspeedFails4stop : [], cost: 1
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Removed unreachable and leaf rules:
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	      0: evalspeedFails4start -> evalspeedFails4bb0in : [], cost: 1
6.79/3.15	
6.79/3.15	      1: evalspeedFails4bb0in -> evalspeedFails41 : A'=free, [], cost: 1
6.79/3.15	
6.79/3.15	      2: evalspeedFails41 -> evalspeedFails42 : [], cost: 1
6.79/3.15	
6.79/3.15	      3: evalspeedFails42 -> evalspeedFails43 : [], cost: 1
6.79/3.15	
6.79/3.15	      4: evalspeedFails43 -> evalspeedFails44 : [], cost: 1
6.79/3.15	
6.79/3.15	      5: evalspeedFails44 -> evalspeedFails45 : B'=1, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	      6: evalspeedFails44 -> evalspeedFails45 : B'=-1, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	      7: evalspeedFails45 -> evalspeedFails46 : [], cost: 1
6.79/3.15	
6.79/3.15	      8: evalspeedFails46 -> evalspeedFails47 : [], cost: 1
6.79/3.15	
6.79/3.15	      9: evalspeedFails47 -> evalspeedFails4bb1in : C'=D, [], cost: 1
6.79/3.15	
6.79/3.15	     10: evalspeedFails4bb1in -> evalspeedFails4bb2in : [ E>=C ], cost: 1
6.79/3.15	
6.79/3.15	     12: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C+B, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	     13: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C-B, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	### Simplification by acceleration and chaining ###
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Eliminated locations (on linear paths):
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	     18: evalspeedFails4start -> evalspeedFails44 : A'=free, [], cost: 5
6.79/3.15	
6.79/3.15	      5: evalspeedFails44 -> evalspeedFails45 : B'=1, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	      6: evalspeedFails44 -> evalspeedFails45 : B'=-1, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	     20: evalspeedFails45 -> evalspeedFails4bb1in : C'=D, [], cost: 3
6.79/3.15	
6.79/3.15	     10: evalspeedFails4bb1in -> evalspeedFails4bb2in : [ E>=C ], cost: 1
6.79/3.15	
6.79/3.15	     12: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C+B, [ A>=1 ], cost: 1
6.79/3.15	
6.79/3.15	     13: evalspeedFails4bb2in -> evalspeedFails4bb1in : C'=C-B, [ 0>=A ], cost: 1
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Eliminated locations (on tree-shaped paths):
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	     21: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=1, [ free>=1 ], cost: 6
6.79/3.15	
6.79/3.15	     22: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=-1, [ 0>=free ], cost: 6
6.79/3.15	
6.79/3.15	     20: evalspeedFails45 -> evalspeedFails4bb1in : C'=D, [], cost: 3
6.79/3.15	
6.79/3.15	     23: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C+B, [ E>=C && A>=1 ], cost: 2
6.79/3.15	
6.79/3.15	     24: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C-B, [ E>=C && 0>=A ], cost: 2
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Accelerating simple loops of location 9.
6.79/3.15	
6.79/3.15	   Accelerating the following rules:
6.79/3.15	
6.79/3.15	     23: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C+B, [ E>=C && A>=1 ], cost: 2
6.79/3.15	
6.79/3.15	     24: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C-B, [ E>=C && 0>=A ], cost: 2
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	   Found no metering function for rule 23.
6.79/3.15	
6.79/3.15	   Found no metering function for rule 24.
6.79/3.15	
6.79/3.15	   Removing the simple loops:.
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Accelerated all simple loops using metering functions (where possible):
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	     21: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=1, [ free>=1 ], cost: 6
6.79/3.15	
6.79/3.15	     22: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=-1, [ 0>=free ], cost: 6
6.79/3.15	
6.79/3.15	     20: evalspeedFails45 -> evalspeedFails4bb1in : C'=D, [], cost: 3
6.79/3.15	
6.79/3.15	     23: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C+B, [ E>=C && A>=1 ], cost: 2
6.79/3.15	
6.79/3.15	     24: evalspeedFails4bb1in -> evalspeedFails4bb1in : C'=C-B, [ E>=C && 0>=A ], cost: 2
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Chained accelerated rules (with incoming rules):
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	     21: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=1, [ free>=1 ], cost: 6
6.79/3.15	
6.79/3.15	     22: evalspeedFails4start -> evalspeedFails45 : A'=free, B'=-1, [ 0>=free ], cost: 6
6.79/3.15	
6.79/3.15	     20: evalspeedFails45 -> evalspeedFails4bb1in : C'=D, [], cost: 3
6.79/3.15	
6.79/3.15	     25: evalspeedFails45 -> evalspeedFails4bb1in : C'=D+B, [ E>=D && A>=1 ], cost: 5
6.79/3.15	
6.79/3.15	     26: evalspeedFails45 -> evalspeedFails4bb1in : C'=D-B, [ E>=D && 0>=A ], cost: 5
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Removed unreachable locations (and leaf rules with constant cost):
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	### Computing asymptotic complexity ###
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Fully simplified ITS problem
6.79/3.15	
6.79/3.15	   Start location: evalspeedFails4start
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	Obtained the following overall complexity (w.r.t. the length of the input n):
6.79/3.15	
6.79/3.15	   Complexity:  Unknown
6.79/3.15	
6.79/3.15	   Cpx degree:  ?
6.79/3.15	
6.79/3.15	   Solved cost: 0
6.79/3.15	
6.79/3.15	   Rule cost:   0
6.79/3.15	
6.79/3.15	   Rule guard:  []
6.79/3.15	
6.79/3.15	
6.79/3.15	
6.79/3.15	WORST_CASE(Omega(0),?)
6.79/3.15	
6.79/3.15	
6.79/3.15	----------------------------------------
6.79/3.15	
6.79/3.15	(2)
6.79/3.15	BOUNDS(1, INF)
6.79/3.18	EOF