8.23/3.80	WORST_CASE(Omega(n^1), O(n^1))
8.23/3.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
8.23/3.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.23/3.81	
8.23/3.81	
8.23/3.81	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
8.23/3.81	
8.23/3.81	(0) CpxIntTrs
8.23/3.81	(1) Koat Proof [FINISHED, 395 ms]
8.23/3.81	(2) BOUNDS(1, n^1)
8.23/3.81	(3) Loat Proof [FINISHED, 2105 ms]
8.23/3.81	(4) BOUNDS(n^1, INF)
8.23/3.81	
8.23/3.81	
8.23/3.81	----------------------------------------
8.23/3.81	
8.23/3.81	(0)
8.23/3.81	Obligation:
8.23/3.81	Complexity Int TRS consisting of the following rules:
8.23/3.81	evalrandom2dstart(A, B, C, D) -> Com_1(evalrandom2dentryin(A, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dentryin(A, B, C, D) -> Com_1(evalrandom2dbb10in(0, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dbb10in(A, B, C, D) -> Com_1(evalrandom2dbbin(A, B, C, D)) :|: B >= A + 1
8.23/3.81	evalrandom2dbb10in(A, B, C, D) -> Com_1(evalrandom2dreturnin(A, B, C, D)) :|: A >= B
8.23/3.81	evalrandom2dbbin(A, B, C, D) -> Com_1(evalrandom2dbb2in(A, B, A + 1, E)) :|: E >= 0 && 3 >= E
8.23/3.81	evalrandom2dbbin(A, B, C, D) -> Com_1(evalrandom2dbb10in(A + 1, B, C, D)) :|: 0 >= E + 1
8.23/3.81	evalrandom2dbbin(A, B, C, D) -> Com_1(evalrandom2dbb10in(A + 1, B, C, D)) :|: E >= 4
8.23/3.81	evalrandom2dbb2in(A, B, C, D) -> Com_1(evalrandom2dNodeBlock9in(A, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dNodeBlock9in(A, B, C, D) -> Com_1(evalrandom2dNodeBlockin(A, B, C, D)) :|: 1 >= D
8.23/3.81	evalrandom2dNodeBlock9in(A, B, C, D) -> Com_1(evalrandom2dNodeBlock7in(A, B, C, D)) :|: D >= 2
8.23/3.81	evalrandom2dNodeBlockin(A, B, C, D) -> Com_1(evalrandom2dLeafBlockin(A, B, C, D)) :|: 0 >= D
8.23/3.81	evalrandom2dNodeBlockin(A, B, C, D) -> Com_1(evalrandom2dLeafBlock1in(A, B, C, D)) :|: D >= 1
8.23/3.81	evalrandom2dLeafBlockin(A, B, C, D) -> Com_1(evalrandom2dbb3in(A, B, C, D)) :|: D >= 0 && D <= 0
8.23/3.81	evalrandom2dLeafBlockin(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: 0 >= D + 1
8.23/3.81	evalrandom2dLeafBlockin(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: D >= 1
8.23/3.81	evalrandom2dbb3in(A, B, C, D) -> Com_1(evalrandom2dbb10in(C, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dLeafBlock1in(A, B, C, D) -> Com_1(evalrandom2dbb5in(A, B, C, D)) :|: D >= 1 && D <= 1
8.23/3.81	evalrandom2dLeafBlock1in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: 0 >= D
8.23/3.81	evalrandom2dLeafBlock1in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: D >= 2
8.23/3.81	evalrandom2dbb5in(A, B, C, D) -> Com_1(evalrandom2dbb10in(C, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dNodeBlock7in(A, B, C, D) -> Com_1(evalrandom2dLeafBlock3in(A, B, C, D)) :|: 2 >= D
8.23/3.81	evalrandom2dNodeBlock7in(A, B, C, D) -> Com_1(evalrandom2dLeafBlock5in(A, B, C, D)) :|: D >= 3
8.23/3.81	evalrandom2dLeafBlock3in(A, B, C, D) -> Com_1(evalrandom2dbb7in(A, B, C, D)) :|: D >= 2 && D <= 2
8.23/3.81	evalrandom2dLeafBlock3in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: 1 >= D
8.23/3.81	evalrandom2dLeafBlock3in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: D >= 3
8.23/3.81	evalrandom2dbb7in(A, B, C, D) -> Com_1(evalrandom2dbb10in(C, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dLeafBlock5in(A, B, C, D) -> Com_1(evalrandom2dbb9in(A, B, C, D)) :|: D >= 3 && D <= 3
8.23/3.81	evalrandom2dLeafBlock5in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: 2 >= D
8.23/3.81	evalrandom2dLeafBlock5in(A, B, C, D) -> Com_1(evalrandom2dNewDefaultin(A, B, C, D)) :|: D >= 4
8.23/3.81	evalrandom2dbb9in(A, B, C, D) -> Com_1(evalrandom2dbb10in(C, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dNewDefaultin(A, B, C, D) -> Com_1(evalrandom2dbb10in(C, B, C, D)) :|: TRUE
8.23/3.81	evalrandom2dreturnin(A, B, C, D) -> Com_1(evalrandom2dstop(A, B, C, D)) :|: TRUE
8.23/3.81	
8.23/3.81	The start-symbols are:[evalrandom2dstart_4]
8.23/3.81	
8.23/3.81	
8.23/3.81	----------------------------------------
8.23/3.81	
8.23/3.81	(1) Koat Proof (FINISHED)
8.23/3.81	YES(?, 27*ar_1 + 6)
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Initial complexity problem:
8.23/3.81	
8.23/3.81	1:	T:
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Testing for reachability in the complexity graph removes the following transitions from problem 1:
8.23/3.81	
8.23/3.81		evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81		evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81		evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81		evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81	We thus obtain the following problem:
8.23/3.81	
8.23/3.81	2:	T:
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Repeatedly propagating knowledge in problem 2 produces the following problem:
8.23/3.81	
8.23/3.81	3:	T:
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)    evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	A polynomial rank function with
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb9in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb10in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb7in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb5in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNewDefaultin) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb3in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock5in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock3in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock1in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlockin) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlock7in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlockin) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlock9in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb2in) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dreturnin) = 1
8.23/3.81	
8.23/3.81		Pol(evalrandom2dstop) = 0
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbbin) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dentryin) = 2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dstart) = 2
8.23/3.81	
8.23/3.81		Pol(koat_start) = 2
8.23/3.81	
8.23/3.81	orients all transitions weakly and the transitions
8.23/3.81	
8.23/3.81		evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81		evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81	strictly and produces the following problem:
8.23/3.81	
8.23/3.81	4:	T:
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)    evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)    evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	A polynomial rank function with
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb9in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb10in) = -V_1 + V_2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb7in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb5in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNewDefaultin) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb3in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock5in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock3in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlock1in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dLeafBlockin) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlock7in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlockin) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dNodeBlock9in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbb2in) = V_2 - V_3
8.23/3.81	
8.23/3.81		Pol(evalrandom2dreturnin) = -V_1 + V_2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dstop) = -V_1 + V_2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dbbin) = -V_1 + V_2 - 1
8.23/3.81	
8.23/3.81		Pol(evalrandom2dentryin) = V_2
8.23/3.81	
8.23/3.81		Pol(evalrandom2dstart) = V_2
8.23/3.81	
8.23/3.81		Pol(koat_start) = V_2
8.23/3.81	
8.23/3.81	orients all transitions weakly and the transition
8.23/3.81	
8.23/3.81		evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81	strictly and produces the following problem:
8.23/3.81	
8.23/3.81	5:	T:
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)       evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ?, Cost: 1)       evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)       evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)    evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)       evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)       evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Repeatedly propagating knowledge in problem 5 produces the following problem:
8.23/3.81	
8.23/3.81	6:	T:
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 4*ar_1, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_2, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb9in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)         evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ e >= 4 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(ar_0 + 1, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_0 + 1, e)) [ e >= 0 /\ 3 >= e ]
8.23/3.81	
8.23/3.81			(Comp: 2, Cost: 1)         evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
8.23/3.81	
8.23/3.81			(Comp: ar_1, Cost: 1)      evalrandom2dbb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)         evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb10in(0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 1)         evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dentryin(ar_0, ar_1, ar_2, ar_3))
8.23/3.81	
8.23/3.81			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
8.23/3.81	
8.23/3.81		start location:	koat_start
8.23/3.81	
8.23/3.81		leaf cost:	0
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Complexity upper bound 27*ar_1 + 6
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Time: 0.365 sec (SMT: 0.302 sec)
8.23/3.81	
8.23/3.81	
8.23/3.81	----------------------------------------
8.23/3.81	
8.23/3.81	(2)
8.23/3.81	BOUNDS(1, n^1)
8.23/3.81	
8.23/3.81	----------------------------------------
8.23/3.81	
8.23/3.81	(3) Loat Proof (FINISHED)
8.23/3.81	
8.23/3.81	
8.23/3.81	### Pre-processing the ITS problem ###
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Initial linear ITS problem
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	      0: evalrandom2dstart -> evalrandom2dentryin : [], cost: 1
8.23/3.81	
8.23/3.81	      1: evalrandom2dentryin -> evalrandom2dbb10in : A'=0, [], cost: 1
8.23/3.81	
8.23/3.81	      2: evalrandom2dbb10in -> evalrandom2dbbin : [ B>=1+A ], cost: 1
8.23/3.81	
8.23/3.81	      3: evalrandom2dbb10in -> evalrandom2dreturnin : [ A>=B ], cost: 1
8.23/3.81	
8.23/3.81	      4: evalrandom2dbbin -> evalrandom2dbb2in : C'=1+A, D'=free, [ free>=0 && 3>=free ], cost: 1
8.23/3.81	
8.23/3.81	      5: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [ 0>=1+free_1 ], cost: 1
8.23/3.81	
8.23/3.81	      6: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [ free_2>=4 ], cost: 1
8.23/3.81	
8.23/3.81	      7: evalrandom2dbb2in -> evalrandom2dNodeBlock9in : [], cost: 1
8.23/3.81	
8.23/3.81	      8: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	      9: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     10: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     11: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     12: evalrandom2dLeafBlockin -> evalrandom2dbb3in : [ D==0 ], cost: 1
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     15: evalrandom2dbb3in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     16: evalrandom2dLeafBlock1in -> evalrandom2dbb5in : [ D==1 ], cost: 1
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     19: evalrandom2dbb5in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     20: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     21: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     22: evalrandom2dLeafBlock3in -> evalrandom2dbb7in : [ D==2 ], cost: 1
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     25: evalrandom2dbb7in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     26: evalrandom2dLeafBlock5in -> evalrandom2dbb9in : [ D==3 ], cost: 1
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     29: evalrandom2dbb9in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     31: evalrandom2dreturnin -> evalrandom2dstop : [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Removed unreachable and leaf rules:
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	      0: evalrandom2dstart -> evalrandom2dentryin : [], cost: 1
8.23/3.81	
8.23/3.81	      1: evalrandom2dentryin -> evalrandom2dbb10in : A'=0, [], cost: 1
8.23/3.81	
8.23/3.81	      2: evalrandom2dbb10in -> evalrandom2dbbin : [ B>=1+A ], cost: 1
8.23/3.81	
8.23/3.81	      4: evalrandom2dbbin -> evalrandom2dbb2in : C'=1+A, D'=free, [ free>=0 && 3>=free ], cost: 1
8.23/3.81	
8.23/3.81	      5: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [ 0>=1+free_1 ], cost: 1
8.23/3.81	
8.23/3.81	      6: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [ free_2>=4 ], cost: 1
8.23/3.81	
8.23/3.81	      7: evalrandom2dbb2in -> evalrandom2dNodeBlock9in : [], cost: 1
8.23/3.81	
8.23/3.81	      8: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	      9: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     10: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     11: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     12: evalrandom2dLeafBlockin -> evalrandom2dbb3in : [ D==0 ], cost: 1
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     15: evalrandom2dbb3in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     16: evalrandom2dLeafBlock1in -> evalrandom2dbb5in : [ D==1 ], cost: 1
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     19: evalrandom2dbb5in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     20: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     21: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     22: evalrandom2dLeafBlock3in -> evalrandom2dbb7in : [ D==2 ], cost: 1
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     25: evalrandom2dbb7in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     26: evalrandom2dLeafBlock5in -> evalrandom2dbb9in : [ D==3 ], cost: 1
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     29: evalrandom2dbb9in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Simplified all rules, resulting in:
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	      0: evalrandom2dstart -> evalrandom2dentryin : [], cost: 1
8.23/3.81	
8.23/3.81	      1: evalrandom2dentryin -> evalrandom2dbb10in : A'=0, [], cost: 1
8.23/3.81	
8.23/3.81	      2: evalrandom2dbb10in -> evalrandom2dbbin : [ B>=1+A ], cost: 1
8.23/3.81	
8.23/3.81	      4: evalrandom2dbbin -> evalrandom2dbb2in : C'=1+A, D'=free, [ free>=0 && 3>=free ], cost: 1
8.23/3.81	
8.23/3.81	      6: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [], cost: 1
8.23/3.81	
8.23/3.81	      7: evalrandom2dbb2in -> evalrandom2dNodeBlock9in : [], cost: 1
8.23/3.81	
8.23/3.81	      8: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	      9: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     10: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     11: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     12: evalrandom2dLeafBlockin -> evalrandom2dbb3in : [ D==0 ], cost: 1
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     15: evalrandom2dbb3in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     16: evalrandom2dLeafBlock1in -> evalrandom2dbb5in : [ D==1 ], cost: 1
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     19: evalrandom2dbb5in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     20: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     21: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     22: evalrandom2dLeafBlock3in -> evalrandom2dbb7in : [ D==2 ], cost: 1
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     25: evalrandom2dbb7in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     26: evalrandom2dLeafBlock5in -> evalrandom2dbb9in : [ D==3 ], cost: 1
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     29: evalrandom2dbb9in -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	### Simplification by acceleration and chaining ###
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Eliminated locations (on linear paths):
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.81	
8.23/3.81	      2: evalrandom2dbb10in -> evalrandom2dbbin : [ B>=1+A ], cost: 1
8.23/3.81	
8.23/3.81	      6: evalrandom2dbbin -> evalrandom2dbb10in : A'=1+A, [], cost: 1
8.23/3.81	
8.23/3.81	     33: evalrandom2dbbin -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ free>=0 && 3>=free ], cost: 2
8.23/3.81	
8.23/3.81	      8: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	      9: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     10: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     11: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     34: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=C, [ D==0 ], cost: 2
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     35: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=C, [ D==1 ], cost: 2
8.23/3.81	
8.23/3.81	     20: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     21: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     36: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=C, [ D==2 ], cost: 2
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     37: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=C, [ D==3 ], cost: 2
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Eliminated locations (on tree-shaped paths):
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.81	
8.23/3.81	     38: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, [ B>=1+A ], cost: 2
8.23/3.81	
8.23/3.81	     39: evalrandom2dbb10in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 3
8.23/3.81	
8.23/3.81	     40: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
8.23/3.81	
8.23/3.81	     41: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
8.23/3.81	
8.23/3.81	     42: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
8.23/3.81	
8.23/3.81	     43: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     34: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=C, [ D==0 ], cost: 2
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     35: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=C, [ D==1 ], cost: 2
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     36: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=C, [ D==2 ], cost: 2
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     37: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=C, [ D==3 ], cost: 2
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Accelerating simple loops of location 2.
8.23/3.81	
8.23/3.81	   Accelerating the following rules:
8.23/3.81	
8.23/3.81	     38: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, [ B>=1+A ], cost: 2
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	   Accelerated rule 38 with metering function -A+B, yielding the new rule 44.
8.23/3.81	
8.23/3.81	   Removing the simple loops: 38.
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Accelerated all simple loops using metering functions (where possible):
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.81	
8.23/3.81	     39: evalrandom2dbb10in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 3
8.23/3.81	
8.23/3.81	     44: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, [ B>=1+A ], cost: -2*A+2*B
8.23/3.81	
8.23/3.81	     40: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
8.23/3.81	
8.23/3.81	     41: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
8.23/3.81	
8.23/3.81	     42: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
8.23/3.81	
8.23/3.81	     43: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     34: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=C, [ D==0 ], cost: 2
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     35: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=C, [ D==1 ], cost: 2
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     36: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=C, [ D==2 ], cost: 2
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     37: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=C, [ D==3 ], cost: 2
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Chained accelerated rules (with incoming rules):
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.81	
8.23/3.81	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.81	
8.23/3.81	     39: evalrandom2dbb10in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 3
8.23/3.81	
8.23/3.81	     40: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
8.23/3.81	
8.23/3.81	     41: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
8.23/3.81	
8.23/3.81	     42: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
8.23/3.81	
8.23/3.81	     43: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     34: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=C, [ D==0 ], cost: 2
8.23/3.81	
8.23/3.81	     47: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=B, [ D==0 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     35: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=C, [ D==1 ], cost: 2
8.23/3.81	
8.23/3.81	     48: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=B, [ D==1 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.81	
8.23/3.81	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.81	
8.23/3.81	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.81	
8.23/3.81	     36: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=C, [ D==2 ], cost: 2
8.23/3.81	
8.23/3.81	     49: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=B, [ D==2 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.81	
8.23/3.81	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.81	
8.23/3.81	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.81	
8.23/3.81	     37: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=C, [ D==3 ], cost: 2
8.23/3.81	
8.23/3.81	     50: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=B, [ D==3 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.81	
8.23/3.81	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.81	
8.23/3.81	     45: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=B, [ B>=1+C ], cost: 1-2*C+2*B
8.23/3.81	
8.23/3.81	
8.23/3.81	
8.23/3.81	Eliminated locations (on tree-shaped paths):
8.23/3.81	
8.23/3.81	   Start location: evalrandom2dstart
8.23/3.81	
8.23/3.81	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.81	
8.23/3.81	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.81	
8.23/3.81	     51: evalrandom2dbb10in -> evalrandom2dLeafBlockin : C'=1+A, D'=free, [ B>=1+A && free>=0 && 0>=free ], cost: 5
8.23/3.81	
8.23/3.81	     52: evalrandom2dbb10in -> evalrandom2dLeafBlock1in : C'=1+A, D'=free, [ B>=1+A && 1>=free && free>=1 ], cost: 5
8.23/3.81	
8.23/3.81	     53: evalrandom2dbb10in -> evalrandom2dLeafBlock3in : C'=1+A, D'=free, [ B>=1+A && free>=2 && 2>=free ], cost: 5
8.23/3.81	
8.23/3.81	     54: evalrandom2dbb10in -> evalrandom2dLeafBlock5in : C'=1+A, D'=free, [ B>=1+A && 3>=free && free>=3 ], cost: 5
8.23/3.81	
8.23/3.81	     13: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
8.23/3.81	
8.23/3.81	     14: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
8.23/3.81	
8.23/3.81	     34: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=C, [ D==0 ], cost: 2
8.23/3.81	
8.23/3.81	     47: evalrandom2dLeafBlockin -> evalrandom2dbb10in : A'=B, [ D==0 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.81	
8.23/3.81	     17: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
8.23/3.81	
8.23/3.81	     18: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
8.23/3.81	
8.23/3.81	     35: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=C, [ D==1 ], cost: 2
8.23/3.81	
8.23/3.81	     48: evalrandom2dLeafBlock1in -> evalrandom2dbb10in : A'=B, [ D==1 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.82	
8.23/3.82	     23: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
8.23/3.82	
8.23/3.82	     24: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
8.23/3.82	
8.23/3.82	     36: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=C, [ D==2 ], cost: 2
8.23/3.82	
8.23/3.82	     49: evalrandom2dLeafBlock3in -> evalrandom2dbb10in : A'=B, [ D==2 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.82	
8.23/3.82	     27: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
8.23/3.82	
8.23/3.82	     28: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
8.23/3.82	
8.23/3.82	     37: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=C, [ D==3 ], cost: 2
8.23/3.82	
8.23/3.82	     50: evalrandom2dLeafBlock5in -> evalrandom2dbb10in : A'=B, [ D==3 && B>=1+C ], cost: 2-2*C+2*B
8.23/3.82	
8.23/3.82	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.82	
8.23/3.82	     45: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=B, [ B>=1+C ], cost: 1-2*C+2*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Eliminated locations (on tree-shaped paths):
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     55: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==0 ], cost: 7
8.23/3.82	
8.23/3.82	     56: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==0 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     57: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==1 ], cost: 7
8.23/3.82	
8.23/3.82	     58: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==1 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     59: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==2 ], cost: 7
8.23/3.82	
8.23/3.82	     60: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==2 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     61: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==3 ], cost: 7
8.23/3.82	
8.23/3.82	     62: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==3 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     30: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=C, [], cost: 1
8.23/3.82	
8.23/3.82	     45: evalrandom2dNewDefaultin -> evalrandom2dbb10in : A'=B, [ B>=1+C ], cost: 1-2*C+2*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Applied pruning (of leafs and parallel rules):
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     56: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==0 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     58: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==1 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     59: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==2 ], cost: 7
8.23/3.82	
8.23/3.82	     60: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==2 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     62: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=free, [ free==3 && B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Accelerating simple loops of location 2.
8.23/3.82	
8.23/3.82	   Simplified some of the simple loops (and removed duplicate rules).
8.23/3.82	
8.23/3.82	   Accelerating the following rules:
8.23/3.82	
8.23/3.82	     56: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=0, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     58: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=1, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     59: evalrandom2dbb10in -> evalrandom2dbb10in : A'=1+A, C'=1+A, D'=2, [ B>=1+A ], cost: 7
8.23/3.82	
8.23/3.82	     60: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=2, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     62: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=3, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	   Found no metering function for rule 56.
8.23/3.82	
8.23/3.82	   Found no metering function for rule 58.
8.23/3.82	
8.23/3.82	   Accelerated rule 59 with metering function -A+B, yielding the new rule 63.
8.23/3.82	
8.23/3.82	   Found no metering function for rule 60.
8.23/3.82	
8.23/3.82	   Found no metering function for rule 62.
8.23/3.82	
8.23/3.82	   Removing the simple loops: 59.
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Accelerated all simple loops using metering functions (where possible):
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     56: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=0, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     58: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=1, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     60: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=2, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     62: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=1+A, D'=3, [ B>=2+A ], cost: 5-2*A+2*B
8.23/3.82	
8.23/3.82	     63: evalrandom2dbb10in -> evalrandom2dbb10in : A'=B, C'=B, D'=2, [ B>=1+A ], cost: -7*A+7*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Chained accelerated rules (with incoming rules):
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     32: evalrandom2dstart -> evalrandom2dbb10in : A'=0, [], cost: 2
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     64: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=0, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     65: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=1, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     66: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=2, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     67: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=3, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     68: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=B, D'=2, [ B>=1 ], cost: 2+7*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Removed unreachable locations (and leaf rules with constant cost):
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     64: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=0, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     65: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=1, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     66: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=2, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     67: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=3, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     68: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=B, D'=2, [ B>=1 ], cost: 2+7*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	### Computing asymptotic complexity ###
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Fully simplified ITS problem
8.23/3.82	
8.23/3.82	   Start location: evalrandom2dstart
8.23/3.82	
8.23/3.82	     46: evalrandom2dstart -> evalrandom2dbb10in : A'=B, [ B>=1 ], cost: 2+2*B
8.23/3.82	
8.23/3.82	     67: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=1, D'=3, [ B>=2 ], cost: 7+2*B
8.23/3.82	
8.23/3.82	     68: evalrandom2dstart -> evalrandom2dbb10in : A'=B, C'=B, D'=2, [ B>=1 ], cost: 2+7*B
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Computing asymptotic complexity for rule 46
8.23/3.82	
8.23/3.82	   Solved the limit problem by the following transformations:
8.23/3.82	
8.23/3.82	      Created initial limit problem:
8.23/3.82	
8.23/3.82	      2+2*B (+), B (+/+!) [not solved]
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	      removing all constraints (solved by SMT)
8.23/3.82	
8.23/3.82	      resulting limit problem: [solved]
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	      applying transformation rule (C) using substitution {B==n}
8.23/3.82	
8.23/3.82	      resulting limit problem:
8.23/3.82	
8.23/3.82	      [solved]
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	   Solution:
8.23/3.82	
8.23/3.82	      B / n
8.23/3.82	
8.23/3.82	   Resulting cost 2+2*n has complexity: Poly(n^1)
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Found new complexity Poly(n^1).
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	Obtained the following overall complexity (w.r.t. the length of the input n):
8.23/3.82	
8.23/3.82	   Complexity:  Poly(n^1)
8.23/3.82	
8.23/3.82	   Cpx degree:  1
8.23/3.82	
8.23/3.82	   Solved cost: 2+2*n
8.23/3.82	
8.23/3.82	   Rule cost:   2+2*B
8.23/3.82	
8.23/3.82	   Rule guard:  [ B>=1 ]
8.23/3.82	
8.23/3.82	
8.23/3.82	
8.23/3.82	WORST_CASE(Omega(n^1),?)
8.23/3.82	
8.23/3.82	
8.23/3.82	----------------------------------------
8.23/3.82	
8.23/3.82	(4)
8.23/3.82	BOUNDS(n^1, INF)
8.31/6.07	EOF