2.12/1.35	WORST_CASE(?, O(n^2))
2.12/1.36	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.12/1.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.12/1.36	
2.12/1.36	
2.12/1.36	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.12/1.36	
2.12/1.36	(0) CpxIntTrs
2.12/1.36	(1) Koat Proof [FINISHED, 75 ms]
2.12/1.36	(2) BOUNDS(1, n^2)
2.12/1.36	
2.12/1.36	
2.12/1.36	----------------------------------------
2.12/1.36	
2.12/1.36	(0)
2.12/1.36	Obligation:
2.12/1.36	Complexity Int TRS consisting of the following rules:
2.12/1.36	eval_foo_start(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_c, v_x, v_y)) :|: TRUE
2.12/1.36	eval_foo_bb0_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_c, v_x, v_y)) :|: v_y > 0
2.12/1.36	eval_foo_bb0_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_c, v_x, v_y)) :|: v_y <= 0
2.12/1.36	eval_foo_bb1_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_c, v_x, v_y)) :|: v_.01 > 0
2.12/1.36	eval_foo_bb1_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_c, v_x, v_y)) :|: v_.01 <= 0
2.12/1.36	eval_foo_bb2_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_y, v_c, v_x, v_y)) :|: v_.01 > v_y
2.12/1.36	eval_foo_bb2_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_c, v_x, v_y)) :|: v_.01 <= v_y
2.12/1.36	eval_foo_bb3_in(v_.01, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_c, v_x, v_y)) :|: TRUE
2.12/1.36	
2.12/1.36	The start-symbols are:[eval_foo_start_4]
2.12/1.36	
2.12/1.36	
2.12/1.36	----------------------------------------
2.12/1.36	
2.12/1.36	(1) Koat Proof (FINISHED)
2.12/1.36	YES(?, 4*ar_0^2 + 4*ar_0*ar_2 + 4*ar_2 + 2*ar_0 + 7)
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	Initial complexity problem:
2.12/1.36	
2.12/1.36	1:	T:
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.12/1.36	
2.12/1.36	2:	T:
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	A polynomial rank function with
2.12/1.36	
2.12/1.36		Pol(evalfoostart) = 2
2.12/1.36	
2.12/1.36		Pol(evalfoobb0in) = 2
2.12/1.36	
2.12/1.36		Pol(evalfoobb1in) = 2
2.12/1.36	
2.12/1.36		Pol(evalfoobb3in) = 1
2.12/1.36	
2.12/1.36		Pol(evalfoobb2in) = 2
2.12/1.36	
2.12/1.36		Pol(evalfoostop) = 0
2.12/1.36	
2.12/1.36		Pol(koat_start) = 2
2.12/1.36	
2.12/1.36	orients all transitions weakly and the transitions
2.12/1.36	
2.12/1.36		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36	strictly and produces the following problem:
2.12/1.36	
2.12/1.36	3:	T:
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	A polynomial rank function with
2.12/1.36	
2.12/1.36		Pol(evalfoobb2in) = -2*V_1 + 2*V_2 - 1
2.12/1.36	
2.12/1.36		Pol(evalfoobb1in) = -2*V_1 + 2*V_2
2.12/1.36	
2.12/1.36	and size complexities
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.12/1.36	
2.12/1.36	orients the transitions
2.12/1.36	
2.12/1.36		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36	weakly and the transition
2.12/1.36	
2.12/1.36		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36	strictly and produces the following problem:
2.12/1.36	
2.12/1.36	4:	T:
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                  evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0 + 2*ar_2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)                  evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                  evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	A polynomial rank function with
2.12/1.36	
2.12/1.36		Pol(evalfoobb2in) = V_2 - 1
2.12/1.36	
2.12/1.36		Pol(evalfoobb1in) = V_2
2.12/1.36	
2.12/1.36	and size complexities
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-1) = ?
2.12/1.36	
2.12/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.12/1.36	
2.12/1.36		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.12/1.36	
2.12/1.36	orients the transitions
2.12/1.36	
2.12/1.36		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36	weakly and the transition
2.12/1.36	
2.12/1.36		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36	strictly and produces the following problem:
2.12/1.36	
2.12/1.36	5:	T:
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0^2 + 2*ar_0*ar_2 + ar_2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                                evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0 + 2*ar_2, Cost: 1)                  evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: ?, Cost: 1)                                evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                                evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)                                koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	Repeatedly propagating knowledge in problem 5 produces the following problem:
2.12/1.36	
2.12/1.36	6:	T:
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 1)                                evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0^2 + 2*ar_0*ar_2 + ar_2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                                evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0 + 2*ar_2, Cost: 1)                  evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_1 >= ar_0 + 1 ]
2.12/1.36	
2.12/1.36			(Comp: 2*ar_0^2 + 2*ar_0*ar_2 + ar_2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 ]
2.12/1.36	
2.12/1.36			(Comp: 2, Cost: 1)                                evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.12/1.36	
2.12/1.36			(Comp: 1, Cost: 0)                                koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.12/1.36	
2.12/1.36		start location:	koat_start
2.12/1.36	
2.12/1.36		leaf cost:	0
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	Complexity upper bound 4*ar_0^2 + 4*ar_0*ar_2 + 4*ar_2 + 2*ar_0 + 7
2.12/1.36	
2.12/1.36	
2.12/1.36	
2.12/1.36	Time: 0.079 sec (SMT: 0.069 sec)
2.12/1.36	
2.12/1.36	
2.12/1.36	----------------------------------------
2.12/1.36	
2.12/1.36	(2)
2.12/1.36	BOUNDS(1, n^2)
2.27/1.38	EOF