2.61/1.51	WORST_CASE(?, O(n^1))
2.61/1.52	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.61/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.52	
2.61/1.52	
2.61/1.52	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.61/1.52	
2.61/1.52	(0) CpxIntTrs
2.61/1.52	(1) Koat Proof [FINISHED, 279 ms]
2.61/1.52	(2) BOUNDS(1, n^1)
2.61/1.52	
2.61/1.52	
2.61/1.52	----------------------------------------
2.61/1.52	
2.61/1.52	(0)
2.61/1.52	Obligation:
2.61/1.52	Complexity Int TRS consisting of the following rules:
2.61/1.52	eval_random1d_start(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb0_in(v_2, v_max, v_x.0)) :|: TRUE
2.61/1.52	eval_random1d_bb0_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, 1)) :|: v_max > 0
2.61/1.52	eval_random1d_bb0_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb3_in(v_2, v_max, v_x.0)) :|: v_max <= 0
2.61/1.52	eval_random1d_bb1_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb2_in(v_2, v_max, v_x.0)) :|: v_x.0 <= v_max
2.61/1.52	eval_random1d_bb1_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb3_in(v_2, v_max, v_x.0)) :|: v_x.0 > v_max
2.61/1.52	eval_random1d_bb2_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_0(v_2, v_max, v_x.0)) :|: TRUE
2.61/1.52	eval_random1d_0(v_2, v_max, v_x.0) -> Com_2(eval_nondet_start(v_2, v_max, v_x.0), eval_random1d_1(nondef.0, v_max, v_x.0)) :|: TRUE
2.61/1.52	eval_random1d_1(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, v_x.0 + 1)) :|: v_2 > 0
2.61/1.52	eval_random1d_1(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, v_x.0 + 1)) :|: v_2 <= 0
2.61/1.52	eval_random1d_bb3_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_stop(v_2, v_max, v_x.0)) :|: TRUE
2.61/1.52	
2.61/1.52	The start-symbols are:[eval_random1d_start_3]
2.61/1.52	
2.61/1.52	
2.61/1.52	----------------------------------------
2.61/1.52	
2.61/1.52	(1) Koat Proof (FINISHED)
2.61/1.52	YES(?, 42*ar_0 + 91)
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	Initial complexity problem:
2.61/1.52	
2.61/1.52	1:	T:
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.52	
2.61/1.52		start location:	koat_start
2.61/1.52	
2.61/1.52		leaf cost:	0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.61/1.52	
2.61/1.52	2:	T:
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.52	
2.61/1.52		start location:	koat_start
2.61/1.52	
2.61/1.52		leaf cost:	0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	A polynomial rank function with
2.61/1.52	
2.61/1.52		Pol(evalrandom1dstart) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb0in) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb1in) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb3in) = 1
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb2in) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1d0) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1d00) = 0
2.61/1.52	
2.61/1.52		Pol(evalnondetstart) = 0
2.61/1.52	
2.61/1.52		Pol(evalrandom1d01) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1d1) = 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1dstop) = 0
2.61/1.52	
2.61/1.52		Pol(koat_start) = 2
2.61/1.52	
2.61/1.52	orients all transitions weakly and the transitions
2.61/1.52	
2.61/1.52		evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52		evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52	strictly and produces the following problem:
2.61/1.52	
2.61/1.52	3:	T:
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)    evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.52	
2.61/1.52		start location:	koat_start
2.61/1.52	
2.61/1.52		leaf cost:	0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.61/1.52	
2.61/1.52	  For symbol evalrandom1d0: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	  For symbol evalrandom1d00: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	  For symbol evalrandom1d01: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	  For symbol evalrandom1d1: X_3 - X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	  For symbol evalrandom1dbb1in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	  For symbol evalrandom1dbb2in: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	This yielded the following problem:
2.61/1.52	
2.61/1.52	4:	T:
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)    evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)    evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52		start location:	koat_start
2.61/1.52	
2.61/1.52		leaf cost:	0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	A polynomial rank function with
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb2in) = 6*V_1 - 6*V_2 + 5
2.61/1.52	
2.61/1.52		Pol(evalrandom1d0) = 6*V_1 - 6*V_2 + 4
2.61/1.52	
2.61/1.52		Pol(evalrandom1dbb1in) = 6*V_1 - 6*V_2 + 6
2.61/1.52	
2.61/1.52		Pol(evalrandom1d1) = 6*V_1 - 6*V_2 + 1
2.61/1.52	
2.61/1.52		Pol(evalrandom1d01) = 6*V_1 - 6*V_2 + 2
2.61/1.52	
2.61/1.52		Pol(evalrandom1d00) = 1
2.61/1.52	
2.61/1.52		Pol(evalnondetstart) = 0
2.61/1.52	
2.61/1.52	and size complexities
2.61/1.52	
2.61/1.52		S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.61/1.52	
2.61/1.52		S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.61/1.52	
2.61/1.52		S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = 1
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.61/1.52	
2.61/1.52		S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.61/1.52	
2.61/1.52		S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.61/1.52	
2.61/1.52		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.61/1.52	
2.61/1.52		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.61/1.52	
2.61/1.52		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.61/1.52	
2.61/1.52		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.61/1.52	
2.61/1.52	orients the transitions
2.61/1.52	
2.61/1.52		evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52		evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52		evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52		evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52	weakly and the transitions
2.61/1.52	
2.61/1.52		evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52		evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52		evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52		evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52		evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52	strictly and produces the following problem:
2.61/1.52	
2.61/1.52	5:	T:
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)              evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.61/1.52	
2.61/1.52			(Comp: 2, Cost: 1)              evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ]
2.61/1.52	
2.61/1.52			(Comp: 6*ar_0 + 12, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)              evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)              evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]
2.61/1.52	
2.61/1.52			(Comp: 1, Cost: 1)              evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))
2.61/1.52	
2.61/1.52		start location:	koat_start
2.61/1.52	
2.61/1.52		leaf cost:	0
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	Complexity upper bound 42*ar_0 + 91
2.61/1.52	
2.61/1.52	
2.61/1.52	
2.61/1.52	Time: 0.297 sec (SMT: 0.242 sec)
2.61/1.52	
2.61/1.52	
2.61/1.52	----------------------------------------
2.61/1.52	
2.61/1.52	(2)
2.61/1.52	BOUNDS(1, n^1)
2.63/1.54	EOF