2.09/1.71	WORST_CASE(?, O(1))
2.62/1.72	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.62/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.62/1.72	
2.62/1.72	
2.62/1.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.62/1.72	
2.62/1.72	(0) CpxIntTrs
2.62/1.72	(1) Koat Proof [FINISHED, 481 ms]
2.62/1.72	(2) BOUNDS(1, 1)
2.62/1.72	
2.62/1.72	
2.62/1.72	----------------------------------------
2.62/1.72	
2.62/1.72	(0)
2.62/1.72	Obligation:
2.62/1.72	Complexity Int TRS consisting of the following rules:
2.62/1.72	eval_foo_start(v_.0, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_x)) :|: TRUE
2.62/1.72	eval_foo_bb0_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_x)) :|: TRUE
2.62/1.72	eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_x)) :|: v_.0 > 0
2.62/1.72	eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_x)) :|: v_.0 <= 0
2.62/1.72	eval_foo_bb2_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(-(2) * v_.0 + 10, v_x)) :|: TRUE
2.62/1.72	eval_foo_bb3_in(v_.0, v_x) -> Com_1(eval_foo_stop(v_.0, v_x)) :|: TRUE
2.62/1.72	
2.62/1.72	The start-symbols are:[eval_foo_start_2]
2.62/1.72	
2.62/1.72	
2.62/1.72	----------------------------------------
2.62/1.72	
2.62/1.72	(1) Koat Proof (FINISHED)
2.62/1.72	YES(?, 42)
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Initial complexity problem:
2.62/1.72	
2.62/1.72	1:	T:
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.62/1.72	
2.62/1.72	2:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	A polynomial rank function with
2.62/1.72	
2.62/1.72		Pol(evalfoostart) = 2
2.62/1.72	
2.62/1.72		Pol(evalfoobb0in) = 2
2.62/1.72	
2.62/1.72		Pol(evalfoobb1in) = 2
2.62/1.72	
2.62/1.72		Pol(evalfoobb2in) = 2
2.62/1.72	
2.62/1.72		Pol(evalfoobb3in) = 1
2.62/1.72	
2.62/1.72		Pol(evalfoostop) = 0
2.62/1.72	
2.62/1.72		Pol(koat_start) = 2
2.62/1.72	
2.62/1.72	orients all transitions weakly and the transitions
2.62/1.72	
2.62/1.72		evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.62/1.72	
2.62/1.72		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72	strictly and produces the following problem:
2.62/1.72	
2.62/1.72	3:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.62/1.72	
2.62/1.72	  For symbol evalfoobb2in: X_1 - 1 >= 0
2.62/1.72	
2.62/1.72	  For symbol evalfoobb3in: -X_1 >= 0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	This yielded the following problem:
2.62/1.72	
2.62/1.72	4:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	5:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Testing for reachability in the complexity graph removes the following transition from problem 5:
2.62/1.72	
2.62/1.72		evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	6:	T:
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] with all transitions in problem 6, the following new transition is obtained:
2.62/1.72	
2.62/1.72		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	7:	T:
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Testing for reachability in the complexity graph removes the following transition from problem 7:
2.62/1.72	
2.62/1.72		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	8:	T:
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 0 >= ar_0 ] with all transitions in problem 8, the following new transition is obtained:
2.62/1.72	
2.62/1.72		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	9:	T:
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Testing for reachability in the complexity graph removes the following transition from problem 9:
2.62/1.72	
2.62/1.72		evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	10:	T:
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) [ 0 <= 0 ] with all transitions in problem 10, the following new transition is obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	11:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Testing for reachability in the complexity graph removes the following transition from problem 11:
2.62/1.72	
2.62/1.72		evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	12:	T:
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) [ 0 <= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) [ 0 <= 0 ] with all transitions in problem 12, the following new transitions are obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	13:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 ] with all transitions in problem 13, the following new transitions are obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ 0 >= -2*ar_1 + 10 /\ 2*ar_1 - 10 >= 0 ]
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	14:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 6)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ 0 >= -2*ar_1 + 10 /\ 2*ar_1 - 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 6)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 ] with all transitions in problem 14, the following new transitions are obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoostop(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 0 >= 4*ar_1 - 10 /\ -4*ar_1 + 10 >= 0 ]
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	15:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 8)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 0 >= 4*ar_1 - 10 /\ -4*ar_1 + 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 8)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 6)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ 0 >= -2*ar_1 + 10 /\ 2*ar_1 - 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	By chaining the transition koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 ] with all transitions in problem 15, the following new transitions are obtained:
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ 0 >= -8*ar_1 + 30 /\ 8*ar_1 - 30 >= 0 ]
2.62/1.72	
2.62/1.72		koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(16*ar_1 - 50, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ -8*ar_1 + 30 >= 1 /\ -8*ar_1 + 29 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	16:	T:
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 10)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ 0 >= -8*ar_1 + 30 /\ 8*ar_1 - 30 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 10)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(16*ar_1 - 50, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ -8*ar_1 + 30 >= 1 /\ -8*ar_1 + 29 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 8)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 0 >= 4*ar_1 - 10 /\ -4*ar_1 + 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 6)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ 0 >= -2*ar_1 + 10 /\ 2*ar_1 - 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: ?, Cost: 2)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Testing for reachability in the complexity graph removes the following transition from problem 16:
2.62/1.72	
2.62/1.72		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb1in(-2*ar_0 + 10, ar_1)) [ ar_0 >= 1 /\ ar_0 - 1 >= 0 ]
2.62/1.72	
2.62/1.72	We thus obtain the following problem:
2.62/1.72	
2.62/1.72	17:	T:
2.62/1.72	
2.62/1.72			(Comp: 2, Cost: 2)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) [ 0 >= ar_0 /\ -ar_0 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 10)    koat_start(ar_0, ar_1) -> Com_1(evalfoobb1in(16*ar_1 - 50, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ -8*ar_1 + 30 >= 1 /\ -8*ar_1 + 29 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 10)    koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-8*ar_1 + 30, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 4*ar_1 - 10 >= 1 /\ 4*ar_1 - 11 >= 0 /\ 0 >= -8*ar_1 + 30 /\ 8*ar_1 - 30 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 8)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(4*ar_1 - 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ -2*ar_1 + 10 >= 1 /\ -2*ar_1 + 9 >= 0 /\ 0 >= 4*ar_1 - 10 /\ -4*ar_1 + 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 6)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(-2*ar_1 + 10, ar_1)) [ 0 <= 0 /\ ar_1 >= 1 /\ ar_1 - 1 >= 0 /\ 0 >= -2*ar_1 + 10 /\ 2*ar_1 - 10 >= 0 ]
2.62/1.72	
2.62/1.72			(Comp: 1, Cost: 4)     koat_start(ar_0, ar_1) -> Com_1(evalfoostop(ar_1, ar_1)) [ 0 <= 0 /\ 0 >= ar_1 /\ -ar_1 >= 0 ]
2.62/1.72	
2.62/1.72		start location:	koat_start
2.62/1.72	
2.62/1.72		leaf cost:	0
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Complexity upper bound 42
2.62/1.72	
2.62/1.72	
2.62/1.72	
2.62/1.72	Time: 0.471 sec (SMT: 0.440 sec)
2.62/1.72	
2.62/1.72	
2.62/1.72	----------------------------------------
2.62/1.72	
2.62/1.72	(2)
2.62/1.72	BOUNDS(1, 1)
2.62/1.74	EOF