2.24/1.37	WORST_CASE(?, O(n^1))
2.24/1.38	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.24/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.24/1.38	
2.24/1.38	
2.24/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.24/1.38	
2.24/1.38	(0) CpxIntTrs
2.24/1.38	(1) Koat Proof [FINISHED, 74 ms]
2.24/1.38	(2) BOUNDS(1, n^1)
2.24/1.38	
2.24/1.38	
2.24/1.38	----------------------------------------
2.24/1.38	
2.24/1.38	(0)
2.24/1.38	Obligation:
2.24/1.38	Complexity Int TRS consisting of the following rules:
2.24/1.38	eval_foo_start(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x1, v_x2)) :|: TRUE
2.24/1.38	eval_foo_bb0_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb1_in(v_x1, v_.01, v_x1, v_x2)) :|: TRUE
2.24/1.38	eval_foo_bb1_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb2_in(v_.0, 1000, v_x1, v_x2)) :|: v_.0 <= 10
2.24/1.38	eval_foo_bb1_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_x1, v_x2)) :|: v_.0 > 10
2.24/1.38	eval_foo_bb2_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x1, v_x2)) :|: v_.01 > 1
2.24/1.38	eval_foo_bb2_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_x1, v_x2)) :|: v_.01 <= 1
2.24/1.38	eval_foo_bb3_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 - 1, v_x1, v_x2)) :|: TRUE
2.24/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_x1, v_x2)) :|: TRUE
2.24/1.38	eval_foo_bb5_in(v_.0, v_.01, v_x1, v_x2) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x1, v_x2)) :|: TRUE
2.24/1.38	
2.24/1.38	The start-symbols are:[eval_foo_start_4]
2.24/1.38	
2.24/1.38	
2.24/1.38	----------------------------------------
2.24/1.38	
2.24/1.38	(1) Koat Proof (FINISHED)
2.24/1.38	YES(?, 2005*ar_1 + 22061)
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Initial complexity problem:
2.24/1.38	
2.24/1.38	1:	T:
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.24/1.38	
2.24/1.38	2:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoostart) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb0in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb1in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb5in) = 1
2.24/1.38	
2.24/1.38		Pol(evalfoobb3in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb4in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoostop) = 0
2.24/1.38	
2.24/1.38		Pol(koat_start) = 2
2.24/1.38	
2.24/1.38	orients all transitions weakly and the transitions
2.24/1.38	
2.24/1.38		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38	strictly and produces the following problem:
2.24/1.38	
2.24/1.38	3:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoostart) = -V_2 + 11
2.24/1.38	
2.24/1.38		Pol(evalfoobb0in) = -V_2 + 11
2.24/1.38	
2.24/1.38		Pol(evalfoobb1in) = -V_1 + 11
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = -V_1 + 10
2.24/1.38	
2.24/1.38		Pol(evalfoobb5in) = -V_1
2.24/1.38	
2.24/1.38		Pol(evalfoobb3in) = -V_1 + 10
2.24/1.38	
2.24/1.38		Pol(evalfoobb4in) = -V_1 + 10
2.24/1.38	
2.24/1.38		Pol(evalfoostop) = -V_1
2.24/1.38	
2.24/1.38		Pol(koat_start) = -V_2 + 11
2.24/1.38	
2.24/1.38	orients all transitions weakly and the transition
2.24/1.38	
2.24/1.38		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38	strictly and produces the following problem:
2.24/1.38	
2.24/1.38	4:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)            evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)            evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ar_1 + 11, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)            evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)            evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)            evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)            evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)            evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)            evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoobb4in) = 1
2.24/1.38	
2.24/1.38		Pol(evalfoobb1in) = 0
2.24/1.38	
2.24/1.38		Pol(evalfoobb3in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = 2
2.24/1.38	
2.24/1.38	and size complexities
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-0) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-2) = 1000
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.24/1.38	
2.24/1.38	orients the transitions
2.24/1.38	
2.24/1.38		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38	weakly and the transitions
2.24/1.38	
2.24/1.38		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38	strictly and produces the following problem:
2.24/1.38	
2.24/1.38	5:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ar_1 + 11, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)              evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoobb3in) = V_3 - 1
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = V_3
2.24/1.38	
2.24/1.38	and size complexities
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = 3*ar_1 + 1782
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 3*ar_1 + 198
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-0) = 3*ar_1 + 198
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-0) = 3*ar_1 + 198
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-0) = 3*ar_1 + 198
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-0) = 3*ar_1 + 594
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]", 0-2) = ?
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-0) = 3*ar_1 + 198
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]", 0-2) = 1000
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.24/1.38	
2.24/1.38		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.24/1.38	
2.24/1.38	orients the transitions
2.24/1.38	
2.24/1.38		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38	weakly and the transition
2.24/1.38	
2.24/1.38		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38	strictly and produces the following problem:
2.24/1.38	
2.24/1.38	6:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)                    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)                    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ar_1 + 11, Cost: 1)            evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)                    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: 1000*ar_1 + 11000, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)          evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)                    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)          evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)                    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)                    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.24/1.38	
2.24/1.38	7:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)                    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)                    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: ar_1 + 11, Cost: 1)            evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1000)) [ 10 >= ar_0 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)                    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 11 ]
2.24/1.38	
2.24/1.38			(Comp: 1000*ar_1 + 11000, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)          evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
2.24/1.38	
2.24/1.38			(Comp: 1000*ar_1 + 11000, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 - 1))
2.24/1.38	
2.24/1.38			(Comp: 2*ar_1 + 22, Cost: 1)          evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)                    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)                    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Complexity upper bound 2005*ar_1 + 22061
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Time: 0.089 sec (SMT: 0.080 sec)
2.24/1.38	
2.24/1.38	
2.24/1.38	----------------------------------------
2.24/1.38	
2.24/1.38	(2)
2.24/1.38	BOUNDS(1, n^1)
2.39/1.39	EOF