2.68/1.88	WORST_CASE(?, O(n^1))
2.68/1.89	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.68/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.68/1.89	
2.68/1.89	
2.68/1.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.68/1.89	
2.68/1.89	(0) CpxIntTrs
2.68/1.89	(1) Koat Proof [FINISHED, 486 ms]
2.68/1.89	(2) BOUNDS(1, n^1)
2.68/1.89	
2.68/1.89	
2.68/1.89	----------------------------------------
2.68/1.89	
2.68/1.89	(0)
2.68/1.89	Obligation:
2.68/1.89	Complexity Int TRS consisting of the following rules:
2.68/1.89	eval_foo_start(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_b, v_x)) :|: TRUE
2.68/1.89	eval_foo_bb0_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_b, v_b, v_x)) :|: TRUE
2.68/1.89	eval_foo_bb1_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_b, v_x)) :|: v_.01 < 0
2.68/1.89	eval_foo_bb1_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_b, v_x)) :|: v_.01 > 0
2.68/1.89	eval_foo_bb1_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_b, v_x)) :|: v_.01 >= 0 && v_.01 <= 0
2.68/1.89	eval_foo_bb2_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_0(v_.0, v_.01, v_b, v_x)) :|: TRUE
2.68/1.89	eval_foo_0(v_.0, v_.01, v_b, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_b, v_x), eval_foo_1(v_.0, v_.01, v_b, v_x)) :|: TRUE
2.68/1.89	eval_foo_1(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 1, 1, v_b, v_x)) :|: v_.0 - 1 >= 0
2.68/1.89	eval_foo_1(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 1, 0, v_b, v_x)) :|: v_.0 - 1 < 0
2.68/1.89	eval_foo_bb3_in(v_.0, v_.01, v_b, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_b, v_x)) :|: TRUE
2.68/1.89	
2.68/1.89	The start-symbols are:[eval_foo_start_4]
2.68/1.89	
2.68/1.89	
2.68/1.89	----------------------------------------
2.68/1.89	
2.68/1.89	(1) Koat Proof (FINISHED)
2.68/1.89	YES(?, 8*ar_1 + ar_3 + 13)
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Initial complexity problem:
2.68/1.89	
2.68/1.89	1:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.68/1.89	
2.68/1.89	2:	T:
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	A polynomial rank function with
2.68/1.89	
2.68/1.89		Pol(evalfoostart) = 2
2.68/1.89	
2.68/1.89		Pol(evalfoobb0in) = 2
2.68/1.89	
2.68/1.89		Pol(evalfoobb1in) = 2
2.68/1.89	
2.68/1.89		Pol(evalfoobb2in) = 2
2.68/1.89	
2.68/1.89		Pol(evalfoobb3in) = 1
2.68/1.89	
2.68/1.89		Pol(evalfoo0) = 2
2.68/1.89	
2.68/1.89		Pol(evalVERIFIERnondetintstart) = 0
2.68/1.89	
2.68/1.89		Pol(evalfoo1) = 2
2.68/1.89	
2.68/1.89		Pol(evalfoostop) = 0
2.68/1.89	
2.68/1.89		Pol(koat_start) = 2
2.68/1.89	
2.68/1.89	orients all transitions weakly and the transitions
2.68/1.89	
2.68/1.89		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
2.68/1.89	
2.68/1.89	strictly and produces the following problem:
2.68/1.89	
2.68/1.89	3:	T:
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	A polynomial rank function with
2.68/1.89	
2.68/1.89		Pol(evalfoobb2in) = 1
2.68/1.89	
2.68/1.89		Pol(evalfoo0) = 1
2.68/1.89	
2.68/1.89		Pol(evalfoobb1in) = V_3
2.68/1.89	
2.68/1.89		Pol(evalfoo1) = 1
2.68/1.89	
2.68/1.89		Pol(evalVERIFIERnondetintstart) = 0
2.68/1.89	
2.68/1.89	and size complexities
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]", 0-2) = 1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_3 + 1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 1-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 1-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 1-2) = ar_3 + 1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))", 1-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_3 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ar_3 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.68/1.89	
2.68/1.89		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.68/1.89	
2.68/1.89		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89	orients the transitions
2.68/1.89	
2.68/1.89		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89		evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89	weakly and the transition
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89	strictly and produces the following problem:
2.68/1.89	
2.68/1.89	4:	T:
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.68/1.89	
2.68/1.89	  For symbol evalfoo0: -X_1 + X_2 >= 0
2.68/1.89	
2.68/1.89	  For symbol evalfoo1: -X_1 + X_2 >= 0
2.68/1.89	
2.68/1.89	  For symbol evalfoobb1in: -X_1 + X_2 >= 0
2.68/1.89	
2.68/1.89	  For symbol evalfoobb2in: -X_1 + X_2 >= 0
2.68/1.89	
2.68/1.89	  For symbol evalfoobb3in: -X_3 >= 0 /\ X_3 >= 0 /\ -X_1 + X_2 >= 0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	This yielded the following problem:
2.68/1.89	
2.68/1.89	5:	T:
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained:
2.68/1.89	
2.68/1.89		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89	We thus obtain the following problem:
2.68/1.89	
2.68/1.89	6:	T:
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Testing for reachability in the complexity graph removes the following transition from problem 6:
2.68/1.89	
2.68/1.89		evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.68/1.89	
2.68/1.89	We thus obtain the following problem:
2.68/1.89	
2.68/1.89	7:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	By chaining the transition evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ] with all transitions in problem 7, the following new transition is obtained:
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89	We thus obtain the following problem:
2.68/1.89	
2.68/1.89	8:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 2)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Repeatedly propagating knowledge in problem 8 produces the following problem:
2.68/1.89	
2.68/1.89	9:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 2)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	By chaining the transition evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ] with all transitions in problem 9, the following new transition is obtained:
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89	We thus obtain the following problem:
2.68/1.89	
2.68/1.89	10:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 3)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Repeatedly propagating knowledge in problem 10 produces the following problem:
2.68/1.89	
2.68/1.89	11:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 3)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	By chaining the transition evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ] with all transitions in problem 11, the following new transition is obtained:
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89	We thus obtain the following problem:
2.68/1.89	
2.68/1.89	12:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 4)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Repeatedly propagating knowledge in problem 12 produces the following problem:
2.68/1.89	
2.68/1.89	13:	T:
2.68/1.89	
2.68/1.89			(Comp: ?, Cost: 4)           evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	A polynomial rank function with
2.68/1.89	
2.68/1.89		Pol(evalfoo1) = V_1
2.68/1.89	
2.68/1.89		Pol(evalVERIFIERnondetintstart) = 0
2.68/1.89	
2.68/1.89	and size complexities
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.68/1.89	
2.68/1.89		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 = 0 ]", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 = 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 = 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\\ ar_2 >= 0 /\\ -ar_0 + ar_1 >= 0 ]", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\\ ar_2 >= 0 /\\ -ar_0 + ar_1 >= 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\\ ar_2 >= 0 /\\ -ar_0 + ar_1 >= 0 ]", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\\ ar_2 >= 0 /\\ -ar_0 + ar_1 >= 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 1-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 1-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 1-2) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]", 1-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-0) = ar_1 + 1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-2) = 0
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 0-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 0-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 0-2) = 1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 0-3) = ar_3
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 1-0) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 1-1) = ar_1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 1-2) = 1
2.68/1.89	
2.68/1.89		S("evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ 1 >= 1 ]", 1-3) = ar_3
2.68/1.89	
2.68/1.89	orients the transitions
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89	weakly and the transition
2.68/1.89	
2.68/1.89		evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89	strictly and produces the following problem:
2.68/1.89	
2.68/1.89	14:	T:
2.68/1.89	
2.68/1.89			(Comp: 2*ar_1, Cost: 4)      evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0 - 1, ar_1, 1, ar_3), evalfoo1(ar_0 - 1, ar_1, 1, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ -ar_0 + ar_1 + 1 >= 0 /\ 1 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: ar_3 + 1, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, 0, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoo0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3), evalfoo1(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 >= 0 /\ ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 + 1 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.68/1.89	
2.68/1.89			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_2 = 0 ]
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.68/1.89	
2.68/1.89			(Comp: 1, Cost: 1)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.68/1.89	
2.68/1.89		start location:	koat_start
2.68/1.89	
2.68/1.89		leaf cost:	0
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Complexity upper bound 8*ar_1 + ar_3 + 13
2.68/1.89	
2.68/1.89	
2.68/1.89	
2.68/1.89	Time: 0.508 sec (SMT: 0.411 sec)
2.68/1.89	
2.68/1.89	
2.68/1.89	----------------------------------------
2.68/1.89	
2.68/1.89	(2)
2.68/1.89	BOUNDS(1, n^1)
2.68/1.91	EOF