2.53/1.84	WORST_CASE(?, O(n^1))
2.53/1.85	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.53/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.53/1.85	
2.53/1.85	
2.53/1.85	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.53/1.85	
2.53/1.85	(0) CpxIntTrs
2.53/1.85	(1) Koat Proof [FINISHED, 287 ms]
2.53/1.85	(2) BOUNDS(1, n^1)
2.53/1.85	
2.53/1.85	
2.53/1.85	----------------------------------------
2.53/1.85	
2.53/1.85	(0)
2.53/1.85	Obligation:
2.53/1.85	Complexity Int TRS consisting of the following rules:
2.53/1.85	eval_peed_pldi09_fig4_2_start(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb0_in(v_m, v_n, v_va.0, v_vb.0)) :|: TRUE
2.53/1.85	eval_peed_pldi09_fig4_2_bb0_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb4_in(v_m, v_n, v_va.0, v_vb.0)) :|: v_m <= 0
2.53/1.85	eval_peed_pldi09_fig4_2_bb0_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb1_in(v_m, v_n, v_n, 0)) :|: v_m > 0
2.53/1.85	eval_peed_pldi09_fig4_2_bb1_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb2_in(v_m, v_n, v_va.0, v_vb.0)) :|: v_va.0 > 0
2.53/1.85	eval_peed_pldi09_fig4_2_bb1_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb4_in(v_m, v_n, v_va.0, v_vb.0)) :|: v_va.0 <= 0
2.53/1.85	eval_peed_pldi09_fig4_2_bb2_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb3_in(v_m, v_n, v_va.0, v_vb.0)) :|: v_vb.0 < v_m
2.53/1.85	eval_peed_pldi09_fig4_2_bb2_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb1_in(v_m, v_n, v_va.0, 0)) :|: v_vb.0 >= v_m
2.53/1.85	eval_peed_pldi09_fig4_2_bb3_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_bb1_in(v_m, v_n, v_va.0 - 1, v_vb.0 + 1)) :|: TRUE
2.53/1.85	eval_peed_pldi09_fig4_2_bb4_in(v_m, v_n, v_va.0, v_vb.0) -> Com_1(eval_peed_pldi09_fig4_2_stop(v_m, v_n, v_va.0, v_vb.0)) :|: TRUE
2.53/1.85	
2.53/1.85	The start-symbols are:[eval_peed_pldi09_fig4_2_start_4]
2.53/1.85	
2.53/1.85	
2.53/1.85	----------------------------------------
2.53/1.85	
2.53/1.85	(1) Koat Proof (FINISHED)
2.53/1.85	YES(?, 28*ar_2 + 11)
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	Initial complexity problem:
2.53/1.85	
2.53/1.85	1:	T:
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.53/1.85	
2.53/1.85		start location:	koat_start
2.53/1.85	
2.53/1.85		leaf cost:	0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.53/1.85	
2.53/1.85	2:	T:
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.53/1.85	
2.53/1.85		start location:	koat_start
2.53/1.85	
2.53/1.85		leaf cost:	0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	A polynomial rank function with
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42start) = 2
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb0in) = 2
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb4in) = 1
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb1in) = 2
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb2in) = 2
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb3in) = 2
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42stop) = 0
2.53/1.85	
2.53/1.85		Pol(koat_start) = 2
2.53/1.85	
2.53/1.85	orients all transitions weakly and the transitions
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85	strictly and produces the following problem:
2.53/1.85	
2.53/1.85	3:	T:
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)    evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.53/1.85	
2.53/1.85		start location:	koat_start
2.53/1.85	
2.53/1.85		leaf cost:	0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.53/1.85	
2.53/1.85	  For symbol evalpeedpldi09fig42bb1in: X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 - 1 >= 0
2.53/1.85	
2.53/1.85	  For symbol evalpeedpldi09fig42bb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.53/1.85	
2.53/1.85	  For symbol evalpeedpldi09fig42bb3in: X_1 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	This yielded the following problem:
2.53/1.85	
2.53/1.85	4:	T:
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)    evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85			(Comp: ?, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)    evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85		start location:	koat_start
2.53/1.85	
2.53/1.85		leaf cost:	0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	A polynomial rank function with
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb3in) = 7*V_2 + 4*V_4 - 1
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb1in) = 7*V_2 + 4*V_4 + 1
2.53/1.85	
2.53/1.85		Pol(evalpeedpldi09fig42bb2in) = 7*V_2 + 4*V_4
2.53/1.85	
2.53/1.85	and size complexities
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-3) = 0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-3) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-3) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 + ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_0 + ar_3
2.53/1.85	
2.53/1.85		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.53/1.85	
2.53/1.85		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.53/1.85	
2.53/1.85		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.53/1.85	
2.53/1.85		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.53/1.85	
2.53/1.85	orients the transitions
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85	weakly and the transitions
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85		evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85	strictly and produces the following problem:
2.53/1.85	
2.53/1.85	5:	T:
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)             evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42stop(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85			(Comp: 7*ar_2 + 1, Cost: 1)    evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.85	
2.53/1.85			(Comp: 7*ar_2 + 1, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: 7*ar_2 + 1, Cost: 1)    evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
2.53/1.85	
2.53/1.85			(Comp: 2, Cost: 1)             evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
2.53/1.85	
2.53/1.85			(Comp: 7*ar_2 + 1, Cost: 1)    evalpeedpldi09fig42bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)             evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)             evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.53/1.85	
2.53/1.85			(Comp: 1, Cost: 1)             evalpeedpldi09fig42start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig42bb0in(ar_0, ar_1, ar_2, ar_3))
2.53/1.85	
2.53/1.85		start location:	koat_start
2.53/1.85	
2.53/1.85		leaf cost:	0
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	Complexity upper bound 28*ar_2 + 11
2.53/1.85	
2.53/1.85	
2.53/1.85	
2.53/1.85	Time: 0.250 sec (SMT: 0.214 sec)
2.53/1.85	
2.53/1.85	
2.53/1.85	----------------------------------------
2.53/1.85	
2.53/1.85	(2)
2.53/1.85	BOUNDS(1, n^1)
2.61/1.88	EOF