2.23/1.34	WORST_CASE(?, O(n^1))
2.23/1.36	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.23/1.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.23/1.36	
2.23/1.36	
2.23/1.36	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.23/1.36	
2.23/1.36	(0) CpxIntTrs
2.23/1.36	(1) Koat Proof [FINISHED, 75 ms]
2.23/1.36	(2) BOUNDS(1, n^1)
2.23/1.36	
2.23/1.36	
2.23/1.36	----------------------------------------
2.23/1.36	
2.23/1.36	(0)
2.23/1.36	Obligation:
2.23/1.36	Complexity Int TRS consisting of the following rules:
2.23/1.36	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
2.23/1.36	eval_foo_bb0_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.1, v_x, v_y)) :|: TRUE
2.23/1.36	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_.01, v_x, v_y)) :|: v_.0 > 0
2.23/1.36	eval_foo_bb1_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_.0 <= 0
2.23/1.36	eval_foo_bb2_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.1 > 0
2.23/1.36	eval_foo_bb2_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 <= 0
2.23/1.36	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 - 1, v_x, v_y)) :|: TRUE
2.23/1.36	eval_foo_bb4_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.1, v_.1, v_x, v_y)) :|: TRUE
2.23/1.36	eval_foo_bb5_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
2.23/1.36	
2.23/1.36	The start-symbols are:[eval_foo_start_5]
2.23/1.36	
2.23/1.36	
2.23/1.36	----------------------------------------
2.23/1.36	
2.23/1.36	(1) Koat Proof (FINISHED)
2.23/1.36	YES(?, 5*ar_1 + 2*ar_3 + 11)
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	Initial complexity problem:
2.23/1.36	
2.23/1.36	1:	T:
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.23/1.36	
2.23/1.36	2:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	A polynomial rank function with
2.23/1.36	
2.23/1.36		Pol(evalfoostart) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb0in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb1in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb2in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb5in) = 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb3in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb4in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoostop) = 0
2.23/1.36	
2.23/1.36		Pol(koat_start) = 2
2.23/1.36	
2.23/1.36	orients all transitions weakly and the transitions
2.23/1.36	
2.23/1.36		evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36	strictly and produces the following problem:
2.23/1.36	
2.23/1.36	3:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	A polynomial rank function with
2.23/1.36	
2.23/1.36		Pol(evalfoostart) = V_2 + 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb0in) = V_2 + 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb1in) = V_1 + 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb2in) = V_1
2.23/1.36	
2.23/1.36		Pol(evalfoobb5in) = V_1
2.23/1.36	
2.23/1.36		Pol(evalfoobb3in) = V_1
2.23/1.36	
2.23/1.36		Pol(evalfoobb4in) = V_1
2.23/1.36	
2.23/1.36		Pol(evalfoostop) = V_1
2.23/1.36	
2.23/1.36		Pol(koat_start) = V_2 + 1
2.23/1.36	
2.23/1.36	orients all transitions weakly and the transition
2.23/1.36	
2.23/1.36		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36	strictly and produces the following problem:
2.23/1.36	
2.23/1.36	4:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ar_1 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)           evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)           evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	A polynomial rank function with
2.23/1.36	
2.23/1.36		Pol(evalfoobb4in) = 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb1in) = 0
2.23/1.36	
2.23/1.36		Pol(evalfoobb3in) = 2
2.23/1.36	
2.23/1.36		Pol(evalfoobb2in) = 2
2.23/1.36	
2.23/1.36	and size complexities
2.23/1.36	
2.23/1.36		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
2.23/1.36	
2.23/1.36		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
2.23/1.36	
2.23/1.36		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
2.23/1.36	
2.23/1.36		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]", 0-0) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]", 0-2) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]", 0-4) = ?
2.23/1.36	
2.23/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-0) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-2) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-4) = ar_4
2.23/1.36	
2.23/1.36		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
2.23/1.36	
2.23/1.36		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.23/1.36	
2.23/1.36		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.23/1.36	
2.23/1.36		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.23/1.36	
2.23/1.36		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.23/1.36	
2.23/1.36	orients the transitions
2.23/1.36	
2.23/1.36		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36	weakly and the transitions
2.23/1.36	
2.23/1.36		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36	strictly and produces the following problem:
2.23/1.36	
2.23/1.36	5:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ar_1 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	A polynomial rank function with
2.23/1.36	
2.23/1.36		Pol(evalfoostart) = V_4
2.23/1.36	
2.23/1.36		Pol(evalfoobb0in) = V_4
2.23/1.36	
2.23/1.36		Pol(evalfoobb1in) = V_3
2.23/1.36	
2.23/1.36		Pol(evalfoobb2in) = V_5
2.23/1.36	
2.23/1.36		Pol(evalfoobb5in) = V_3
2.23/1.36	
2.23/1.36		Pol(evalfoobb3in) = V_5 - 1
2.23/1.36	
2.23/1.36		Pol(evalfoobb4in) = V_5
2.23/1.36	
2.23/1.36		Pol(evalfoostop) = V_3
2.23/1.36	
2.23/1.36		Pol(koat_start) = V_4
2.23/1.36	
2.23/1.36	orients all transitions weakly and the transition
2.23/1.36	
2.23/1.36		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36	strictly and produces the following problem:
2.23/1.36	
2.23/1.36	6:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ar_1 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ar_3, Cost: 1)          evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.23/1.36	
2.23/1.36	7:	T:
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: ar_1 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_2)) [ ar_0 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.23/1.36	
2.23/1.36			(Comp: ar_3, Cost: 1)          evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ]
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]
2.23/1.36	
2.23/1.36			(Comp: ar_3, Cost: 1)          evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
2.23/1.36	
2.23/1.36			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.23/1.36	
2.23/1.36			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.23/1.36	
2.23/1.36		start location:	koat_start
2.23/1.36	
2.23/1.36		leaf cost:	0
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	Complexity upper bound 5*ar_1 + 2*ar_3 + 11
2.23/1.36	
2.23/1.36	
2.23/1.36	
2.23/1.36	Time: 0.114 sec (SMT: 0.095 sec)
2.23/1.36	
2.23/1.36	
2.23/1.36	----------------------------------------
2.23/1.36	
2.23/1.36	(2)
2.23/1.36	BOUNDS(1, n^1)
2.23/1.37	EOF