2.19/1.29	WORST_CASE(?, O(1))
2.19/1.30	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.19/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.19/1.30	
2.19/1.30	
2.19/1.30	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.19/1.30	
2.19/1.30	(0) CpxIntTrs
2.19/1.30	(1) Koat Proof [FINISHED, 77 ms]
2.19/1.30	(2) BOUNDS(1, 1)
2.19/1.30	
2.19/1.30	
2.19/1.30	----------------------------------------
2.19/1.30	
2.19/1.30	(0)
2.19/1.30	Obligation:
2.19/1.30	Complexity Int TRS consisting of the following rules:
2.19/1.30	eval_foo_start(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.1, v_i, v_j)) :|: TRUE
2.19/1.30	eval_foo_bb0_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb1_in(0, 3, v_.1, v_i, v_j)) :|: TRUE
2.19/1.30	eval_foo_bb1_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.01, v_i, v_j)) :|: v_.0 < 10
2.19/1.30	eval_foo_bb1_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_i, v_j)) :|: v_.0 >= 10
2.19/1.30	eval_foo_bb2_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_i, v_j)) :|: v_.1 < 12
2.19/1.30	eval_foo_bb2_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_i, v_j)) :|: v_.1 >= 12
2.19/1.30	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 1, v_i, v_j)) :|: TRUE
2.19/1.30	eval_foo_bb4_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.1, v_.1, v_i, v_j)) :|: TRUE
2.19/1.30	eval_foo_bb5_in(v_.0, v_.01, v_.1, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.1, v_i, v_j)) :|: TRUE
2.19/1.30	
2.19/1.30	The start-symbols are:[eval_foo_start_5]
2.19/1.30	
2.19/1.30	
2.19/1.30	----------------------------------------
2.19/1.30	
2.19/1.30	(1) Koat Proof (FINISHED)
2.19/1.30	YES(?, 74)
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	Initial complexity problem:
2.19/1.30	
2.19/1.30	1:	T:
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.19/1.30	
2.19/1.30	2:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	A polynomial rank function with
2.19/1.30	
2.19/1.30		Pol(evalfoostart) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb0in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb1in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb2in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb5in) = 1
2.19/1.30	
2.19/1.30		Pol(evalfoobb3in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb4in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoostop) = 0
2.19/1.30	
2.19/1.30		Pol(koat_start) = 2
2.19/1.30	
2.19/1.30	orients all transitions weakly and the transitions
2.19/1.30	
2.19/1.30		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30	strictly and produces the following problem:
2.19/1.30	
2.19/1.30	3:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	A polynomial rank function with
2.19/1.30	
2.19/1.30		Pol(evalfoostart) = 10
2.19/1.30	
2.19/1.30		Pol(evalfoobb0in) = 10
2.19/1.30	
2.19/1.30		Pol(evalfoobb1in) = -V_1 + 10
2.19/1.30	
2.19/1.30		Pol(evalfoobb2in) = -V_1 + 9
2.19/1.30	
2.19/1.30		Pol(evalfoobb5in) = -V_1
2.19/1.30	
2.19/1.30		Pol(evalfoobb3in) = -V_1 + 9
2.19/1.30	
2.19/1.30		Pol(evalfoobb4in) = -V_1 + 9
2.19/1.30	
2.19/1.30		Pol(evalfoostop) = -V_1
2.19/1.30	
2.19/1.30		Pol(koat_start) = 10
2.19/1.30	
2.19/1.30	orients all transitions weakly and the transition
2.19/1.30	
2.19/1.30		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30	strictly and produces the following problem:
2.19/1.30	
2.19/1.30	4:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	A polynomial rank function with
2.19/1.30	
2.19/1.30		Pol(evalfoobb4in) = 1
2.19/1.30	
2.19/1.30		Pol(evalfoobb1in) = 0
2.19/1.30	
2.19/1.30		Pol(evalfoobb3in) = 2
2.19/1.30	
2.19/1.30		Pol(evalfoobb2in) = 2
2.19/1.30	
2.19/1.30	and size complexities
2.19/1.30	
2.19/1.30		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.19/1.30	
2.19/1.30		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.19/1.30	
2.19/1.30		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.19/1.30	
2.19/1.30		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]", 0-0) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]", 0-1) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]", 0-2) = ?
2.19/1.30	
2.19/1.30		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))", 0-0) = 0
2.19/1.30	
2.19/1.30		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))", 0-1) = 3
2.19/1.30	
2.19/1.30		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))", 0-2) = ar_2
2.19/1.30	
2.19/1.30		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.19/1.30	
2.19/1.30		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.19/1.30	
2.19/1.30		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.19/1.30	
2.19/1.30	orients the transitions
2.19/1.30	
2.19/1.30		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30	weakly and the transitions
2.19/1.30	
2.19/1.30		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30	strictly and produces the following problem:
2.19/1.30	
2.19/1.30	5:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	A polynomial rank function with
2.19/1.30	
2.19/1.30		Pol(evalfoostart) = 9
2.19/1.30	
2.19/1.30		Pol(evalfoobb0in) = 9
2.19/1.30	
2.19/1.30		Pol(evalfoobb1in) = -V_2 + 12
2.19/1.30	
2.19/1.30		Pol(evalfoobb2in) = -V_3 + 12
2.19/1.30	
2.19/1.30		Pol(evalfoobb5in) = -V_2
2.19/1.30	
2.19/1.30		Pol(evalfoobb3in) = -V_3 + 11
2.19/1.30	
2.19/1.30		Pol(evalfoobb4in) = -V_3 + 12
2.19/1.30	
2.19/1.30		Pol(evalfoostop) = -V_2
2.19/1.30	
2.19/1.30		Pol(koat_start) = 9
2.19/1.30	
2.19/1.30	orients all transitions weakly and the transition
2.19/1.30	
2.19/1.30		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30	strictly and produces the following problem:
2.19/1.30	
2.19/1.30	6:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: 9, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: ?, Cost: 1)     evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.19/1.30	
2.19/1.30	7:	T:
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(0, 3, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_1)) [ 9 >= ar_0 ]
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
2.19/1.30	
2.19/1.30			(Comp: 9, Cost: 1)     evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 11 >= ar_2 ]
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 12 ]
2.19/1.30	
2.19/1.30			(Comp: 9, Cost: 1)     evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1))
2.19/1.30	
2.19/1.30			(Comp: 20, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_2, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.30	
2.19/1.30			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.30	
2.19/1.30		start location:	koat_start
2.19/1.30	
2.19/1.30		leaf cost:	0
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	Complexity upper bound 74
2.19/1.30	
2.19/1.30	
2.19/1.30	
2.19/1.30	Time: 0.089 sec (SMT: 0.080 sec)
2.19/1.30	
2.19/1.30	
2.19/1.30	----------------------------------------
2.19/1.30	
2.19/1.30	(2)
2.19/1.30	BOUNDS(1, 1)
2.34/1.33	EOF