2.24/1.74	WORST_CASE(?, O(n^2))
2.24/1.75	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.24/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.24/1.75	
2.24/1.75	
2.24/1.75	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.24/1.75	
2.24/1.75	(0) CpxIntTrs
2.24/1.75	(1) Koat Proof [FINISHED, 85 ms]
2.24/1.75	(2) BOUNDS(1, n^2)
2.24/1.75	
2.24/1.75	
2.24/1.75	----------------------------------------
2.24/1.75	
2.24/1.75	(0)
2.24/1.75	Obligation:
2.24/1.75	Complexity Int TRS consisting of the following rules:
2.24/1.75	eval_foo_start(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE
2.24/1.75	eval_foo_bb0_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_.01, v_1, v_x, v_y)) :|: TRUE
2.24/1.75	eval_foo_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 >= 0
2.24/1.75	eval_foo_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 < 0
2.24/1.75	eval_foo_bb2_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, 1, v_.0 + 1, v_x, v_y)) :|: TRUE
2.24/1.75	eval_foo_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 >= v_.01
2.24/1.75	eval_foo_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 < v_.01
2.24/1.75	eval_foo_bb4_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01 + 1, v_1, v_x, v_y)) :|: TRUE
2.24/1.75	eval_foo_bb5_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_1 - 2, v_.01, v_1, v_x, v_y)) :|: TRUE
2.24/1.75	eval_foo_bb6_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE
2.24/1.75	
2.24/1.75	The start-symbols are:[eval_foo_start_5]
2.24/1.75	
2.24/1.75	
2.24/1.75	----------------------------------------
2.24/1.75	
2.24/1.75	(1) Koat Proof (FINISHED)
2.24/1.75	YES(?, 754*ar_1 + 12*ar_1^2 + 1466)
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Initial complexity problem:
2.24/1.75	
2.24/1.75	1:	T:
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.24/1.75	
2.24/1.75	2:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	A polynomial rank function with
2.24/1.75	
2.24/1.75		Pol(evalfoostart) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb0in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb1in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb2in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb6in) = 1
2.24/1.75	
2.24/1.75		Pol(evalfoobb3in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb4in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb5in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoostop) = 0
2.24/1.75	
2.24/1.75		Pol(koat_start) = 2
2.24/1.75	
2.24/1.75	orients all transitions weakly and the transitions
2.24/1.75	
2.24/1.75		evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75	strictly and produces the following problem:
2.24/1.75	
2.24/1.75	3:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	A polynomial rank function with
2.24/1.75	
2.24/1.75		Pol(evalfoostart) = V_2 + 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb0in) = V_2 + 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb1in) = V_1 + 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb2in) = V_1 + 1
2.24/1.75	
2.24/1.75		Pol(evalfoobb6in) = V_1
2.24/1.75	
2.24/1.75		Pol(evalfoobb3in) = V_4
2.24/1.75	
2.24/1.75		Pol(evalfoobb4in) = V_4
2.24/1.75	
2.24/1.75		Pol(evalfoobb5in) = V_4
2.24/1.75	
2.24/1.75		Pol(evalfoostop) = V_1
2.24/1.75	
2.24/1.75		Pol(koat_start) = V_2 + 2
2.24/1.75	
2.24/1.75	orients all transitions weakly and the transition
2.24/1.75	
2.24/1.75		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75	strictly and produces the following problem:
2.24/1.75	
2.24/1.75	4:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)           evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.24/1.75	
2.24/1.75	5:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)           evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)           evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	A polynomial rank function with
2.24/1.75	
2.24/1.75		Pol(evalfoobb5in) = 1
2.24/1.75	
2.24/1.75		Pol(evalfoobb1in) = 0
2.24/1.75	
2.24/1.75		Pol(evalfoobb4in) = 2
2.24/1.75	
2.24/1.75		Pol(evalfoobb3in) = 2
2.24/1.75	
2.24/1.75	and size complexities
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-2) = 1
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-0) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-3) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75	orients the transitions
2.24/1.75	
2.24/1.75		evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75	weakly and the transitions
2.24/1.75	
2.24/1.75		evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75	strictly and produces the following problem:
2.24/1.75	
2.24/1.75	6:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)             evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	A polynomial rank function with
2.24/1.75	
2.24/1.75		Pol(evalfoobb4in) = -V_3 + V_4
2.24/1.75	
2.24/1.75		Pol(evalfoobb3in) = -V_3 + V_4 + 1
2.24/1.75	
2.24/1.75	and size complexities
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 6*ar_1 + 12960
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 6*ar_1 + 6*ar_3 + 77760
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-0) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))", 0-3) = 6*ar_1 + 2160
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = 6*ar_1 + 12960
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-0) = 6*ar_1 + 77760
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-3) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-0) = 6*ar_1 + 12960
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-3) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-0) = 6*ar_1 + 2160
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-2) = 1
2.24/1.75	
2.24/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))", 0-3) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = 6*ar_1 + 2160
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = 6*ar_1 + 6*ar_3 + 12960
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-0) = 6*ar_1 + 360
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-2) = ?
2.24/1.75	
2.24/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-3) = 6*ar_1 + 6*ar_3 + 12960
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.24/1.75	
2.24/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75		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
2.24/1.75	
2.24/1.75	orients the transitions
2.24/1.75	
2.24/1.75		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75	weakly and the transition
2.24/1.75	
2.24/1.75		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75	strictly and produces the following problem:
2.24/1.75	
2.24/1.75	7:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)                            evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)                            evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)                     evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)                            evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)                     evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: 6*ar_1^2 + 374*ar_1 + 724, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)                   evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ?, Cost: 1)                            evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)                   evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)                            evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.24/1.75	
2.24/1.75	8:	T:
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)                            evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 1, Cost: 1)                            evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)                     evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)                            evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: ar_1 + 2, Cost: 1)                     evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1))
2.24/1.75	
2.24/1.75			(Comp: 6*ar_1^2 + 374*ar_1 + 724, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)                   evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.24/1.75	
2.24/1.75			(Comp: 6*ar_1^2 + 374*ar_1 + 724, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2*ar_1 + 4, Cost: 1)                   evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(Comp: 2, Cost: 1)                            evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.24/1.75	
2.24/1.75			(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 ]
2.24/1.75	
2.24/1.75		start location:	koat_start
2.24/1.75	
2.24/1.75		leaf cost:	0
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Complexity upper bound 754*ar_1 + 12*ar_1^2 + 1466
2.24/1.75	
2.24/1.75	
2.24/1.75	
2.24/1.75	Time: 0.118 sec (SMT: 0.100 sec)
2.24/1.75	
2.24/1.75	
2.24/1.75	----------------------------------------
2.24/1.75	
2.24/1.75	(2)
2.24/1.75	BOUNDS(1, n^2)
2.27/1.77	EOF