5.66/2.56	WORST_CASE(Omega(n^1), O(n^1))
5.66/2.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.66/2.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.66/2.57	
5.66/2.57	
5.66/2.57	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.66/2.57	
5.66/2.57	(0) CpxIntTrs
5.66/2.57	(1) Koat Proof [FINISHED, 501 ms]
5.66/2.57	(2) BOUNDS(1, n^1)
5.66/2.57	(3) Loat Proof [FINISHED, 807 ms]
5.66/2.57	(4) BOUNDS(n^1, INF)
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(0)
5.66/2.57	Obligation:
5.66/2.57	Complexity Int TRS consisting of the following rules:
5.66/2.57	eval_start_start(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb0_in(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_bb0_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_0(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_0(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_1(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_1(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_2(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_2(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb1_in(v_x, v_3, v_x, v_y, v_z_0)) :|: v_y >= 0
5.66/2.57	eval_start_2(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb6_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v_y < 0
5.66/2.57	eval_start_bb1_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb2_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v__0 > v_y
5.66/2.57	eval_start_bb1_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb5_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v__0 <= v_y
5.66/2.57	eval_start_bb2_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb3_in(v__0, v__0 - v_y - 1, v_x, v_y, v_y)) :|: TRUE
5.66/2.57	eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb4_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v_z_0 > 0
5.66/2.57	eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb1_in(v_3, v_3, v_x, v_y, v_z_0)) :|: v_z_0 <= 0
5.66/2.57	eval_start_bb4_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0 - 1)) :|: TRUE
5.66/2.57	eval_start_bb5_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_stop(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_bb6_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_8(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_8(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_9(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	eval_start_9(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_stop(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE
5.66/2.57	
5.66/2.57	The start-symbols are:[eval_start_start_5]
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(1) Koat Proof (FINISHED)
5.66/2.57	YES(?, 30*ar_2 + 18)
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Initial complexity problem:
5.66/2.57	
5.66/2.57	1:	T:
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.66/2.57	
5.66/2.57	2:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	A polynomial rank function with
5.66/2.57	
5.66/2.57		Pol(evalstartstart) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartbb0in) = 2
5.66/2.57	
5.66/2.57		Pol(evalstart0) = 2
5.66/2.57	
5.66/2.57		Pol(evalstart1) = 2
5.66/2.57	
5.66/2.57		Pol(evalstart2) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartbb1in) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartbb6in) = 0
5.66/2.57	
5.66/2.57		Pol(evalstartbb2in) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartbb5in) = 1
5.66/2.57	
5.66/2.57		Pol(evalstartbb3in) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartbb4in) = 2
5.66/2.57	
5.66/2.57		Pol(evalstartstop) = 0
5.66/2.57	
5.66/2.57		Pol(evalstart8) = 0
5.66/2.57	
5.66/2.57		Pol(evalstart9) = 0
5.66/2.57	
5.66/2.57		Pol(koat_start) = 2
5.66/2.57	
5.66/2.57	orients all transitions weakly and the transitions
5.66/2.57	
5.66/2.57		evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57	strictly and produces the following problem:
5.66/2.57	
5.66/2.57	3:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0))
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.66/2.57	
5.66/2.57	  For symbol evalstart8: -X_1 - 1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstart9: -X_1 - 1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb1in: -X_2 + X_3 >= 0 /\ X_1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb3in: X_3 - X_5 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb4in: X_3 - X_5 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 3 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 - 2 >= 0 /\ X_2 + X_3 - 4 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb5in: -X_2 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 >= 0
5.66/2.57	
5.66/2.57	  For symbol evalstartbb6in: -X_1 - 1 >= 0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	This yielded the following problem:
5.66/2.57	
5.66/2.57	4:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	A polynomial rank function with
5.66/2.57	
5.66/2.57		Pol(evalstartbb4in) = V_2 + 3*V_3 + 2*V_4 + 2*V_5
5.66/2.57	
5.66/2.57		Pol(evalstartbb3in) = V_2 + 3*V_3 + 2*V_4 + 2*V_5 + 1
5.66/2.57	
5.66/2.57		Pol(evalstartbb1in) = 3*V_2 + 3*V_3 + 1
5.66/2.57	
5.66/2.57		Pol(evalstartbb2in) = 3*V_2 + 3*V_3
5.66/2.57	
5.66/2.57	and size complexities
5.66/2.57	
5.66/2.57		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = ar_2 + ar_3
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-3) = ar_2 + ar_3
5.66/2.57	
5.66/2.57		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-4) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-3) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-4) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-3) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-4) = 0
5.66/2.57	
5.66/2.57		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-4) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_2 + ar_3
5.66/2.57	
5.66/2.57		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
5.66/2.57	
5.66/2.57	orients the transitions
5.66/2.57	
5.66/2.57		evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57	weakly and the transitions
5.66/2.57	
5.66/2.57		evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57	strictly and produces the following problem:
5.66/2.57	
5.66/2.57	5:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)             evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 6*ar_2 + 1, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 6*ar_2 + 1, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ]
5.66/2.57	
5.66/2.57			(Comp: 6*ar_2 + 1, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: 6*ar_2 + 1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)             evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: 6*ar_2 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)             evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Complexity upper bound 30*ar_2 + 18
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Time: 0.491 sec (SMT: 0.371 sec)
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(2)
5.66/2.57	BOUNDS(1, n^1)
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(3) Loat Proof (FINISHED)
5.66/2.57	
5.66/2.57	
5.66/2.57	### Pre-processing the ITS problem ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Initial linear ITS problem
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.66/2.57	
5.66/2.57	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.66/2.57	
5.66/2.57	      2: evalstart0 -> evalstart1 : [], cost: 1
5.66/2.57	
5.66/2.57	      3: evalstart1 -> evalstart2 : [], cost: 1
5.66/2.57	
5.66/2.57	      4: evalstart2 -> evalstartbb1in : B'=C, [ A>=0 ], cost: 1
5.66/2.57	
5.66/2.57	      5: evalstart2 -> evalstartbb6in : [ 0>=1+A ], cost: 1
5.66/2.57	
5.66/2.57	      6: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1
5.66/2.57	
5.66/2.57	      7: evalstartbb1in -> evalstartbb5in : [ A>=B ], cost: 1
5.66/2.57	
5.66/2.57	      8: evalstartbb2in -> evalstartbb3in : D'=-1-A+B, E'=A, [], cost: 1
5.66/2.57	
5.66/2.57	      9: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1
5.66/2.57	
5.66/2.57	     10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1
5.66/2.57	
5.66/2.57	     11: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1
5.66/2.57	
5.66/2.57	     12: evalstartbb5in -> evalstartstop : [], cost: 1
5.66/2.57	
5.66/2.57	     13: evalstartbb6in -> evalstart8 : [], cost: 1
5.66/2.57	
5.66/2.57	     14: evalstart8 -> evalstart9 : [], cost: 1
5.66/2.57	
5.66/2.57	     15: evalstart9 -> evalstartstop : [], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Removed unreachable and leaf rules:
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.66/2.57	
5.66/2.57	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.66/2.57	
5.66/2.57	      2: evalstart0 -> evalstart1 : [], cost: 1
5.66/2.57	
5.66/2.57	      3: evalstart1 -> evalstart2 : [], cost: 1
5.66/2.57	
5.66/2.57	      4: evalstart2 -> evalstartbb1in : B'=C, [ A>=0 ], cost: 1
5.66/2.57	
5.66/2.57	      6: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1
5.66/2.57	
5.66/2.57	      8: evalstartbb2in -> evalstartbb3in : D'=-1-A+B, E'=A, [], cost: 1
5.66/2.57	
5.66/2.57	      9: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1
5.66/2.57	
5.66/2.57	     10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1
5.66/2.57	
5.66/2.57	     11: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	### Simplification by acceleration and chaining ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Eliminated locations (on linear paths):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2
5.66/2.57	
5.66/2.57	     10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1
5.66/2.57	
5.66/2.57	     21: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerating simple loops of location 7.
5.66/2.57	
5.66/2.57	   Accelerating the following rules:
5.66/2.57	
5.66/2.57	     21: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Accelerated rule 21 with metering function E, yielding the new rule 22.
5.66/2.57	
5.66/2.57	   Removing the simple loops: 21.
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerated all simple loops using metering functions (where possible):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2
5.66/2.57	
5.66/2.57	     10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1
5.66/2.57	
5.66/2.57	     22: evalstartbb3in -> evalstartbb3in : E'=0, [ E>=1 ], cost: 2*E
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Chained accelerated rules (with incoming rules):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2
5.66/2.57	
5.66/2.57	     23: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 2+2*A
5.66/2.57	
5.66/2.57	     10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Eliminated locations (on tree-shaped paths):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     24: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=A, [ B>=1+A && 0>=A ], cost: 3
5.66/2.57	
5.66/2.57	     25: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 3+2*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerating simple loops of location 5.
5.66/2.57	
5.66/2.57	   Accelerating the following rules:
5.66/2.57	
5.66/2.57	     24: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=A, [ B>=1+A && 0>=A ], cost: 3
5.66/2.57	
5.66/2.57	     25: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 3+2*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Accelerated rule 24 with metering function -A+B, yielding the new rule 26.
5.66/2.57	
5.66/2.57	   Accelerated rule 25 with backward acceleration, yielding the new rule 27.
5.66/2.57	
5.66/2.57	   Removing the simple loops: 24 25.
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerated all simple loops using metering functions (where possible):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     26: evalstartbb1in -> evalstartbb1in : B'=A+A*(A-B), D'=A+A*(A-B), E'=A, [ B>=1+A && 0>=A ], cost: -3*A+3*B
5.66/2.57	
5.66/2.57	     27: evalstartbb1in -> evalstartbb1in : B'=-A*k-k+B, D'=-A*k-k+B, E'=0, [ B>=1+A && A>=1 && k>0 && 1-k-(-1+k)*A+B>=1+A ], cost: 2*A*k+3*k
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Chained accelerated rules (with incoming rules):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5
5.66/2.57	
5.66/2.57	     28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A
5.66/2.57	
5.66/2.57	     29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Removed unreachable locations (and leaf rules with constant cost):
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A
5.66/2.57	
5.66/2.57	     29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	### Computing asymptotic complexity ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Fully simplified ITS problem
5.66/2.57	
5.66/2.57	   Start location: evalstartstart
5.66/2.57	
5.66/2.57	     28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A
5.66/2.57	
5.66/2.57	     29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Computing asymptotic complexity for rule 28
5.66/2.57	
5.66/2.57	   Solved the limit problem by the following transformations:
5.66/2.57	
5.66/2.57	      Created initial limit problem:
5.66/2.57	
5.66/2.57	      5+3*C-3*A (+), 1-A (+/+!), C-A (+/+!), 1+A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {A==0}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      1 (+/+!), C (+/+!), 5+3*C (+) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {C==1+A}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      1 (+/+!), 8+3*A (+), 1+A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (B), deleting 1 (+/+!)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      8+3*A (+), 1+A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (D), replacing 8+3*A (+) by 3*A (+)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      3*A (+), 1+A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (D), replacing 1+A (+/+!) by A (+)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      3*A (+), A (+) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (A), replacing 3*A (+) by A (+) and 3 (+!) using + limit vector (+,+!)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      3 (+!), A (+) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (B), deleting 3 (+!)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      A (+) [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Solution:
5.66/2.57	
5.66/2.57	      C / 1+n
5.66/2.57	
5.66/2.57	      A / 0
5.66/2.57	
5.66/2.57	   Resulting cost 8+3*n has complexity: Poly(n^1)
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Found new complexity Poly(n^1).
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Computing asymptotic complexity for rule 29
5.66/2.57	
5.66/2.57	   Simplified the guard:
5.66/2.57	
5.66/2.57	     29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k
5.66/2.57	
5.66/2.57	   Solved the limit problem by the following transformations:
5.66/2.57	
5.66/2.57	      Created initial limit problem:
5.66/2.57	
5.66/2.57	      5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      removing all constraints (solved by SMT)
5.66/2.57	
5.66/2.57	      resulting limit problem: [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {C==2*n,A==1,k==n}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Solved the limit problem by the following transformations:
5.66/2.57	
5.66/2.57	      Created initial limit problem:
5.66/2.57	
5.66/2.57	      5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {k==1}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      1 (+/+!), 8+2*A (+), A (+/+!), C-A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (B), deleting 1 (+/+!)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      8+2*A (+), A (+/+!), C-A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      removing all constraints (solved by SMT)
5.66/2.57	
5.66/2.57	      resulting limit problem: [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {C==n,A==-1+n}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Solved the limit problem by the following transformations:
5.66/2.57	
5.66/2.57	      Created initial limit problem:
5.66/2.57	
5.66/2.57	      5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {A==1}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      1 (+/+!), 1+C-2*k (+/+!), k (+/+!), 5+5*k (+) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (B), deleting 1 (+/+!)
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      1+C-2*k (+/+!), k (+/+!), 5+5*k (+) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      removing all constraints (solved by SMT)
5.66/2.57	
5.66/2.57	      resulting limit problem: [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {C==2*n,k==n}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Solution:
5.66/2.57	
5.66/2.57	      C / 2*n
5.66/2.57	
5.66/2.57	      A / 1
5.66/2.57	
5.66/2.57	      k / n
5.66/2.57	
5.66/2.57	   Resulting cost 5+5*n has complexity: Poly(n^1)
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Obtained the following overall complexity (w.r.t. the length of the input n):
5.66/2.57	
5.66/2.57	   Complexity:  Poly(n^1)
5.66/2.57	
5.66/2.57	   Cpx degree:  1
5.66/2.57	
5.66/2.57	   Solved cost: 8+3*n
5.66/2.57	
5.66/2.57	   Rule cost:   5+3*C-3*A
5.66/2.57	
5.66/2.57	   Rule guard:  [ -A==0 && C>=1+A ]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	WORST_CASE(Omega(n^1),?)
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(4)
5.66/2.57	BOUNDS(n^1, INF)
5.66/2.59	EOF