2.02/1.30	WORST_CASE(?, O(n^1))
2.02/1.31	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.02/1.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.02/1.31	
2.02/1.31	
2.02/1.31	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.02/1.31	
2.02/1.31	(0) CpxIntTrs
2.02/1.31	(1) Koat Proof [FINISHED, 77 ms]
2.02/1.31	(2) BOUNDS(1, n^1)
2.02/1.31	
2.02/1.31	
2.02/1.31	----------------------------------------
2.02/1.31	
2.02/1.31	(0)
2.02/1.31	Obligation:
2.02/1.31	Complexity Int TRS consisting of the following rules:
2.02/1.31	eval_foo_start(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_i, v_j)) :|: TRUE
2.02/1.31	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_i, v_.01, v_i, v_j)) :|: TRUE
2.02/1.31	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, 0, v_i, v_j)) :|: v_.0 < 5
2.02/1.31	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_i, v_j)) :|: v_.0 >= 5
2.02/1.31	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_i, v_j)) :|: v_.0 > 2 && v_.01 <= 9
2.02/1.31	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_i, v_j)) :|: v_.0 <= 2
2.02/1.31	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_i, v_j)) :|: v_.01 > 9
2.02/1.31	eval_foo_bb3_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 + 1, v_i, v_j)) :|: TRUE
2.02/1.31	eval_foo_bb4_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_i, v_j)) :|: TRUE
2.02/1.31	eval_foo_bb5_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_i, v_j)) :|: TRUE
2.02/1.31	
2.02/1.31	The start-symbols are:[eval_foo_start_4]
2.02/1.31	
2.02/1.31	
2.02/1.31	----------------------------------------
2.02/1.31	
2.02/1.31	(1) Koat Proof (FINISHED)
2.02/1.31	YES(?, 56*ar_1 + 258)
2.02/1.31	
2.02/1.31	
2.02/1.31	
2.02/1.31	Initial complexity problem:
2.02/1.31	
2.02/1.31	1:	T:
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.31	
2.02/1.31		start location:	koat_start
2.02/1.31	
2.02/1.31		leaf cost:	0
2.02/1.31	
2.02/1.31	
2.02/1.31	
2.02/1.31	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.02/1.31	
2.02/1.31	2:	T:
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.31	
2.02/1.31		start location:	koat_start
2.02/1.31	
2.02/1.31		leaf cost:	0
2.02/1.31	
2.02/1.31	
2.02/1.31	
2.02/1.31	A polynomial rank function with
2.02/1.31	
2.02/1.31		Pol(evalfoostart) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoobb0in) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoobb1in) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoobb2in) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoobb5in) = 1
2.02/1.31	
2.02/1.31		Pol(evalfoobb3in) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoobb4in) = 2
2.02/1.31	
2.02/1.31		Pol(evalfoostop) = 0
2.02/1.31	
2.02/1.31		Pol(koat_start) = 2
2.02/1.31	
2.02/1.31	orients all transitions weakly and the transitions
2.02/1.31	
2.02/1.31		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.31	
2.02/1.31	strictly and produces the following problem:
2.02/1.31	
2.02/1.31	3:	T:
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.31	
2.02/1.31			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.31	
2.02/1.31			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.32	
2.02/1.32		start location:	koat_start
2.02/1.32	
2.02/1.32		leaf cost:	0
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	A polynomial rank function with
2.02/1.32	
2.02/1.32		Pol(evalfoostart) = -2*V_2 + 9
2.02/1.32	
2.02/1.32		Pol(evalfoobb0in) = -2*V_2 + 9
2.02/1.32	
2.02/1.32		Pol(evalfoobb1in) = -2*V_1 + 9
2.02/1.32	
2.02/1.32		Pol(evalfoobb2in) = -2*V_1 + 8
2.02/1.32	
2.02/1.32		Pol(evalfoobb5in) = -2*V_1
2.02/1.32	
2.02/1.32		Pol(evalfoobb3in) = -2*V_1 + 8
2.02/1.32	
2.02/1.32		Pol(evalfoobb4in) = -2*V_1 + 7
2.02/1.32	
2.02/1.32		Pol(evalfoostop) = -2*V_1
2.02/1.32	
2.02/1.32		Pol(koat_start) = -2*V_2 + 9
2.02/1.32	
2.02/1.32	orients all transitions weakly and the transitions
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.32	
2.02/1.32	strictly and produces the following problem:
2.02/1.32	
2.02/1.32	4:	T:
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.32	
2.02/1.32		start location:	koat_start
2.02/1.32	
2.02/1.32		leaf cost:	0
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	A polynomial rank function with
2.02/1.32	
2.02/1.32		Pol(evalfoobb4in) = 1
2.02/1.32	
2.02/1.32		Pol(evalfoobb1in) = 0
2.02/1.32	
2.02/1.32		Pol(evalfoobb3in) = 2
2.02/1.32	
2.02/1.32		Pol(evalfoobb2in) = 2
2.02/1.32	
2.02/1.32	and size complexities
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.02/1.32	
2.02/1.32	orients the transitions
2.02/1.32	
2.02/1.32		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32	weakly and the transitions
2.02/1.32	
2.02/1.32		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32	strictly and produces the following problem:
2.02/1.32	
2.02/1.32	5:	T:
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)     evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)              evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.32	
2.02/1.32		start location:	koat_start
2.02/1.32	
2.02/1.32		leaf cost:	0
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	A polynomial rank function with
2.02/1.32	
2.02/1.32		Pol(evalfoobb3in) = -V_3 + 9
2.02/1.32	
2.02/1.32		Pol(evalfoobb2in) = -V_3 + 10
2.02/1.32	
2.02/1.32	and size complexities
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = 7*ar_1 + 64827
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = 7*ar_1 + 9261
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ?
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = 7*ar_1 + 1323
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.02/1.32	
2.02/1.32		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.02/1.32	
2.02/1.32	orients the transitions
2.02/1.32	
2.02/1.32		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32	weakly and the transition
2.02/1.32	
2.02/1.32		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32	strictly and produces the following problem:
2.02/1.32	
2.02/1.32	6:	T:
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)               evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)               evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.32	
2.02/1.32			(Comp: 20*ar_1 + 90, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32			(Comp: ?, Cost: 1)               evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)     evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)               evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.32	
2.02/1.32		start location:	koat_start
2.02/1.32	
2.02/1.32		leaf cost:	0
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.02/1.32	
2.02/1.32	7:	T:
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)               evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 1)               evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.02/1.32	
2.02/1.32			(Comp: 20*ar_1 + 90, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.02/1.32	
2.02/1.32			(Comp: 2*ar_1 + 9, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.02/1.32	
2.02/1.32			(Comp: 20*ar_1 + 90, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.02/1.32	
2.02/1.32			(Comp: 6*ar_1 + 27, Cost: 1)     evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 2, Cost: 1)               evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.02/1.32	
2.02/1.32			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.02/1.32	
2.02/1.32		start location:	koat_start
2.02/1.32	
2.02/1.32		leaf cost:	0
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	Complexity upper bound 56*ar_1 + 258
2.02/1.32	
2.02/1.32	
2.02/1.32	
2.02/1.32	Time: 0.105 sec (SMT: 0.090 sec)
2.02/1.32	
2.02/1.32	
2.02/1.32	----------------------------------------
2.02/1.32	
2.02/1.32	(2)
2.02/1.32	BOUNDS(1, n^1)
2.22/1.36	EOF