2.07/1.61	WORST_CASE(?, O(n^1))
2.07/1.62	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.07/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.07/1.62	
2.07/1.62	
2.07/1.62	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.07/1.62	
2.07/1.62	(0) CpxIntTrs
2.07/1.62	(1) Koat Proof [FINISHED, 371 ms]
2.07/1.62	(2) BOUNDS(1, n^1)
2.07/1.62	
2.07/1.62	
2.07/1.62	----------------------------------------
2.07/1.62	
2.07/1.62	(0)
2.07/1.62	Obligation:
2.07/1.62	Complexity Int TRS consisting of the following rules:
2.07/1.62	eval_t10_start(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb0_in(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE
2.07/1.62	eval_t10_bb0_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_x, v_y, v_1, v_x, v_y)) :|: TRUE
2.07/1.62	eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb2_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 > v_.01
2.07/1.62	eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb3_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 <= v_.01
2.07/1.62	eval_t10_bb2_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_0(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE
2.07/1.62	eval_t10_0(v_.0, v_.01, v_1, v_x, v_y) -> Com_2(eval_nondet_start(v_.0, v_.01, v_1, v_x, v_y), eval_t10_1(v_.0, v_.01, nondef.0, v_x, v_y)) :|: TRUE
2.07/1.62	eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0, v_.01 + 1, v_1, v_x, v_y)) :|: v_1 > 0
2.07/1.62	eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0 - 1, v_.01 + 1, v_1, v_x, v_y)) :|: v_1 > 0 && v_1 <= 0
2.07/1.62	eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 <= 0 && v_1 > 0
2.07/1.62	eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0 - 1, v_.01, v_1, v_x, v_y)) :|: v_1 <= 0
2.07/1.62	eval_t10_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_stop(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE
2.07/1.62	
2.07/1.62	The start-symbols are:[eval_t10_start_5]
2.07/1.62	
2.07/1.62	
2.07/1.62	----------------------------------------
2.07/1.62	
2.07/1.62	(1) Koat Proof (FINISHED)
2.07/1.62	YES(?, 42*ar_1 + 42*ar_3 + 6)
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Initial complexity problem:
2.07/1.62	
2.07/1.62	1:	T:
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 /\ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 /\ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.07/1.62	
2.07/1.62		evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 /\ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62		evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 /\ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62	We thus obtain the following problem:
2.07/1.62	
2.07/1.62	2:	T:
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.07/1.62	
2.07/1.62	3:	T:
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	A polynomial rank function with
2.07/1.62	
2.07/1.62		Pol(evalt101) = 2
2.07/1.62	
2.07/1.62		Pol(evalt10bb1in) = 2
2.07/1.62	
2.07/1.62		Pol(evalt1001) = 2
2.07/1.62	
2.07/1.62		Pol(evalt1000) = 0
2.07/1.62	
2.07/1.62		Pol(evalnondetstart) = 0
2.07/1.62	
2.07/1.62		Pol(evalt100) = 2
2.07/1.62	
2.07/1.62		Pol(evalt10bb3in) = 1
2.07/1.62	
2.07/1.62		Pol(evalt10stop) = 0
2.07/1.62	
2.07/1.62		Pol(evalt10bb2in) = 2
2.07/1.62	
2.07/1.62		Pol(evalt10bb0in) = 2
2.07/1.62	
2.07/1.62		Pol(evalt10start) = 2
2.07/1.62	
2.07/1.62		Pol(koat_start) = 2
2.07/1.62	
2.07/1.62	orients all transitions weakly and the transitions
2.07/1.62	
2.07/1.62		evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62		evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62	strictly and produces the following problem:
2.07/1.62	
2.07/1.62	4:	T:
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)    evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.07/1.62	
2.07/1.62	  For symbol evalt100: X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt1000: X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt1001: X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt101: X_5 - X_6 >= 0 /\ -X_5 + X_6 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt10bb1in: X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt10bb2in: X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	  For symbol evalt10bb3in: X_3 - X_4 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	This yielded the following problem:
2.07/1.62	
2.07/1.62	5:	T:
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)    evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)    evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: ?, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	A polynomial rank function with
2.07/1.62	
2.07/1.62		Pol(koat_start) = 6*V_2 - 6*V_4
2.07/1.62	
2.07/1.62		Pol(evalt10start) = 6*V_2 - 6*V_4
2.07/1.62	
2.07/1.62		Pol(evalt10bb0in) = 6*V_2 - 6*V_4
2.07/1.62	
2.07/1.62		Pol(evalt10bb1in) = 6*V_1 - 6*V_3
2.07/1.62	
2.07/1.62		Pol(evalt10bb2in) = 6*V_1 - 6*V_3 - 1
2.07/1.62	
2.07/1.62		Pol(evalt10bb3in) = 6*V_1 - 6*V_3
2.07/1.62	
2.07/1.62		Pol(evalt100) = 6*V_1 - 6*V_3 - 2
2.07/1.62	
2.07/1.62		Pol(evalt10stop) = 6*V_1 - 6*V_3
2.07/1.62	
2.07/1.62		Pol(evalt1000) = 1
2.07/1.62	
2.07/1.62		Pol(evalt1001) = 6*V_1 - 6*V_3 - 4
2.07/1.62	
2.07/1.62		Pol(evalnondetstart) = 0
2.07/1.62	
2.07/1.62		Pol(evalt101) = 6*V_1 - 6*V_3 - 5
2.07/1.62	
2.07/1.62	orients all transitions weakly and the transitions
2.07/1.62	
2.07/1.62		evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62		evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62		evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62		evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62		evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62		evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62		evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62	strictly and produces the following problem:
2.07/1.62	
2.07/1.62	6:	T:
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)                  evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 1, Cost: 1)                  evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)                  evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 2, Cost: 1)                  evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ]
2.07/1.62	
2.07/1.62			(Comp: 6*ar_1 + 6*ar_3, Cost: 1)    evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ]
2.07/1.62	
2.07/1.62		start location:	koat_start
2.07/1.62	
2.07/1.62		leaf cost:	0
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Complexity upper bound 42*ar_1 + 42*ar_3 + 6
2.07/1.62	
2.07/1.62	
2.07/1.62	
2.07/1.62	Time: 0.372 sec (SMT: 0.297 sec)
2.07/1.62	
2.07/1.62	
2.07/1.62	----------------------------------------
2.07/1.62	
2.07/1.62	(2)
2.07/1.62	BOUNDS(1, n^1)
2.51/1.65	EOF