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3 changes: 2 additions & 1 deletion Complexity_ITS/Lommen_26/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -5,4 +5,5 @@ The benchmark set consists of the following files:
2. Hershel M. Farkas' variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
3. Hershel M. Farkas' variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)
4. Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
5. Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
5. Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)

4 changes: 2 additions & 2 deletions Complexity_ITS/Lommen_26/collatz.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,5 +6,5 @@
(fun collatz (-> Int Int))
(entrypoint start)
(rule (start n) (collatz n))
(rule (collatz n) (collatz k) :guard (= n (* 2 k)))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (= n (+ (* 2 k) 1)))
(rule (collatz n) (collatz k) :guard (and (> n 1) (= n (* 2 k))))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (and (> n 1) (= n (+ (* 2 k) 1))))
4 changes: 2 additions & 2 deletions Complexity_ITS/Lommen_26/collatz_mod_div.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,5 +6,5 @@
(fun collatz (-> Int Int))
(entrypoint start)
(rule (start n) (collatz n))
(rule (collatz n) (collatz (div n 2)) :guard (= (mod n 2) 0))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (= (mod n 2) 1))
(rule (collatz n) (collatz (div n 2)) :guard (and (> n 1) (= (mod n 2) 0)))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (and (> n 1) (= (mod n 2) 1)))
10 changes: 5 additions & 5 deletions Complexity_ITS/Lommen_26/farkas.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,8 @@
(fun farkas (-> Int Int))
(entrypoint start)
(rule (start n) (farkas n))
(rule (farkas n) (farkas k) :guard (= n (+ (* 3 k) 1)))
(rule (farkas n) (farkas (* 3 k)) :guard (= n (* 6 k)))
(rule (farkas n) (farkas (+ (* 3 k) 1)) :guard (= n (+ (* 6 k) 2)))
(rule (farkas n) (farkas (+ (* 9 k) 5)) :guard (= n (+ (* 6 k) 3)))
(rule (farkas n) (farkas (+ (* 9 k) 8)) :guard (= n (+ (* 6 k) 5)))
(rule (farkas n) (farkas k) :guard (and (> n 1) (= n (+ (* 3 k) 1))))
(rule (farkas n) (farkas (* 3 k)) :guard (and (> n 1) (= n (* 6 k))))
(rule (farkas n) (farkas (+ (* 3 k) 1)) :guard (and (> n 1) (= n (+ (* 6 k) 2))))
(rule (farkas n) (farkas (+ (* 9 k) 5)) :guard (and (> n 1) (= n (+ (* 6 k) 3))))
(rule (farkas n) (farkas (+ (* 9 k) 8)) :guard (and (> n 1) (= n (+ (* 6 k) 5))))
6 changes: 3 additions & 3 deletions Complexity_ITS/Lommen_26/farkas_mod_div.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,6 @@
(fun farkas (-> Int Int))
(entrypoint start)
(rule (start n) (farkas n))
(rule (farkas n) (farkas (div (- n 1) 3)) :guard (= (mod n 3) 1))
(rule (farkas n) (farkas (div n 2)) :guard (or (= (mod n 6) 0) (= (mod n 6) 2)))
(rule (farkas n) (farkas (div (+ (* 3 n) 1) 2)) :guard (or (= (mod n 6) 3) (= (mod n 6) 5)))
(rule (farkas n) (farkas (div (- n 1) 3)) :guard (and (> n 1) (= (mod n 3) 1)))
(rule (farkas n) (farkas (div n 2)) :guard (and (> n 1) (or (= (mod n 6) 0) (= (mod n 6) 2))))
(rule (farkas n) (farkas (div (+ (* 3 n) 1) 2)) :guard (and (> n 1) (or (= (mod n 6) 3) (= (mod n 6) 5))))
8 changes: 4 additions & 4 deletions Complexity_ITS/Lommen_26/syracuse.ari
Original file line number Diff line number Diff line change
@@ -1,11 +1,11 @@
; Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)
; Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)

(format LCTRS)
(theory Ints)
(fun start (-> Int Int))
(fun syracuse (-> Int Int))
(entrypoint start)
(rule (start n) (syracuse n))
(rule (syracuse n) (syracuse (+ (* 6 k) 1)) :guard (= n (+ (* 8 k) 1)))
(rule (syracuse n) (syracuse (+ (* 2 k) 1)) :guard (= n (+ (* 8 k) 5)))
(rule (syracuse n) (syracuse (+ (* 6 k) 5)) :guard (= n (+ (* 4 k) 3)))
(rule (syracuse n) (syracuse (+ (* 6 k) 1)) :guard (and (> n 1) (= n (+ (* 8 k) 1))))
(rule (syracuse n) (syracuse (+ (* 2 k) 1)) :guard (and (> n 1) (= n (+ (* 8 k) 5))))
(rule (syracuse n) (syracuse (+ (* 6 k) 5)) :guard (and (> n 1) (= n (+ (* 4 k) 3))))
8 changes: 4 additions & 4 deletions Complexity_ITS/Lommen_26/syracuse_mod_div.ari
Original file line number Diff line number Diff line change
@@ -1,11 +1,11 @@
; Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
; Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)

(format LCTRS)
(theory Ints)
(fun start (-> Int Int))
(fun syracuse (-> Int Int))
(entrypoint start)
(rule (start n) (syracuse n))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 4)) :guard (= (mod n 8) 1))
(rule (syracuse n) (syracuse (div (- n 1) 4)) :guard (= (mod n 8) 5))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 2)) :guard (= (mod n 4) 3))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 4)) :guard (and (> n 1) (= (mod n 8) 1)))
(rule (syracuse n) (syracuse (div (- n 1) 4)) :guard (and (> n 1) (= (mod n 8) 5)))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 2)) :guard (and (> n 1) (= (mod n 4) 3)))
3 changes: 2 additions & 1 deletion Integer_Transition_Systems/Lommen_26/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -5,4 +5,5 @@ The benchmark set consists of the following files:
2. Hershel M. Farkas' variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
3. Hershel M. Farkas' variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)
4. Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
5. Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
5. Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)

4 changes: 2 additions & 2 deletions Integer_Transition_Systems/Lommen_26/collatz.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,5 +6,5 @@
(fun collatz (-> Int Int))
(entrypoint start)
(rule (start n) (collatz n))
(rule (collatz n) (collatz k) :guard (= n (* 2 k)))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (= n (+ (* 2 k) 1)))
(rule (collatz n) (collatz k) :guard (and (> n 1) (= n (* 2 k))))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (and (> n 1) (= n (+ (* 2 k) 1))))
4 changes: 2 additions & 2 deletions Integer_Transition_Systems/Lommen_26/collatz_mod_div.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,5 +6,5 @@
(fun collatz (-> Int Int))
(entrypoint start)
(rule (start n) (collatz n))
(rule (collatz n) (collatz (div n 2)) :guard (= (mod n 2) 0))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (= (mod n 2) 1))
(rule (collatz n) (collatz (div n 2)) :guard (and (> n 1) (= (mod n 2) 0)))
(rule (collatz n) (collatz (+ (* 3 n) 1)) :guard (and (> n 1) (= (mod n 2) 1)))
10 changes: 5 additions & 5 deletions Integer_Transition_Systems/Lommen_26/farkas.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,8 @@
(fun farkas (-> Int Int))
(entrypoint start)
(rule (start n) (farkas n))
(rule (farkas n) (farkas k) :guard (= n (+ (* 3 k) 1)))
(rule (farkas n) (farkas (* 3 k)) :guard (= n (* 6 k)))
(rule (farkas n) (farkas (+ (* 3 k) 1)) :guard (= n (+ (* 6 k) 2)))
(rule (farkas n) (farkas (+ (* 9 k) 5)) :guard (= n (+ (* 6 k) 3)))
(rule (farkas n) (farkas (+ (* 9 k) 8)) :guard (= n (+ (* 6 k) 5)))
(rule (farkas n) (farkas k) :guard (and (> n 1) (= n (+ (* 3 k) 1))))
(rule (farkas n) (farkas (* 3 k)) :guard (and (> n 1) (= n (* 6 k))))
(rule (farkas n) (farkas (+ (* 3 k) 1)) :guard (and (> n 1) (= n (+ (* 6 k) 2))))
(rule (farkas n) (farkas (+ (* 9 k) 5)) :guard (and (> n 1) (= n (+ (* 6 k) 3))))
(rule (farkas n) (farkas (+ (* 9 k) 8)) :guard (and (> n 1) (= n (+ (* 6 k) 5))))
6 changes: 3 additions & 3 deletions Integer_Transition_Systems/Lommen_26/farkas_mod_div.ari
Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,6 @@
(fun farkas (-> Int Int))
(entrypoint start)
(rule (start n) (farkas n))
(rule (farkas n) (farkas (div (- n 1) 3)) :guard (= (mod n 3) 1))
(rule (farkas n) (farkas (div n 2)) :guard (or (= (mod n 6) 0) (= (mod n 6) 2)))
(rule (farkas n) (farkas (div (+ (* 3 n) 1) 2)) :guard (or (= (mod n 6) 3) (= (mod n 6) 5)))
(rule (farkas n) (farkas (div (- n 1) 3)) :guard (and (> n 1) (= (mod n 3) 1)))
(rule (farkas n) (farkas (div n 2)) :guard (and (> n 1) (or (= (mod n 6) 0) (= (mod n 6) 2))))
(rule (farkas n) (farkas (div (+ (* 3 n) 1) 2)) :guard (and (> n 1) (or (= (mod n 6) 3) (= (mod n 6) 5))))
8 changes: 4 additions & 4 deletions Integer_Transition_Systems/Lommen_26/syracuse.ari
Original file line number Diff line number Diff line change
@@ -1,11 +1,11 @@
; Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)
; Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)

(format LCTRS)
(theory Ints)
(fun start (-> Int Int))
(fun syracuse (-> Int Int))
(entrypoint start)
(rule (start n) (syracuse n))
(rule (syracuse n) (syracuse (+ (* 6 k) 1)) :guard (= n (+ (* 8 k) 1)))
(rule (syracuse n) (syracuse (+ (* 2 k) 1)) :guard (= n (+ (* 8 k) 5)))
(rule (syracuse n) (syracuse (+ (* 6 k) 5)) :guard (= n (+ (* 4 k) 3)))
(rule (syracuse n) (syracuse (+ (* 6 k) 1)) :guard (and (> n 1) (= n (+ (* 8 k) 1))))
(rule (syracuse n) (syracuse (+ (* 2 k) 1)) :guard (and (> n 1) (= n (+ (* 8 k) 5))))
(rule (syracuse n) (syracuse (+ (* 6 k) 5)) :guard (and (> n 1) (= n (+ (* 4 k) 3))))
8 changes: 4 additions & 4 deletions Integer_Transition_Systems/Lommen_26/syracuse_mod_div.ari
Original file line number Diff line number Diff line change
@@ -1,11 +1,11 @@
; Syracuse variant of the Collatz function (see, e.g., https://arxiv.org/pdf/2105.14697)
; Syracuse variant of the Collatz function with mod and div (see, e.g., https://arxiv.org/pdf/2105.14697)

(format LCTRS)
(theory Ints)
(fun start (-> Int Int))
(fun syracuse (-> Int Int))
(entrypoint start)
(rule (start n) (syracuse n))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 4)) :guard (= (mod n 8) 1))
(rule (syracuse n) (syracuse (div (- n 1) 4)) :guard (= (mod n 8) 5))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 2)) :guard (= (mod n 4) 3))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 4)) :guard (and (> n 1) (= (mod n 8) 1)))
(rule (syracuse n) (syracuse (div (- n 1) 4)) :guard (and (> n 1) (= (mod n 8) 5)))
(rule (syracuse n) (syracuse (div (+ (* 3 n) 1) 2)) :guard (and (> n 1) (= (mod n 4) 3)))