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TRS Stand 20472 pair #381710415
details
property
value
status
complete
benchmark
2.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n024.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.301175117493 seconds
cpu usage
0.297561421
max memory
1.4114816E7
stage attributes
key
value
output-size
9916
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !870 : [o * o] --> o !dot : [o * o] --> o admit : [o * o] --> o carry : [o * o * o] --> o cond : [o * o] --> o nil : [] --> o sum : [o * o * o] --> o true : [] --> o w : [] --> o admit(X, nil) => nil admit(X, !dot(Y, !dot(Z, !dot(w, U)))) => cond(!870(sum(X, Y, Z), w), !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U))))) cond(true, X) => X As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: !870 : [fa * s] --> ya !dot : [s * bb] --> bb admit : [pa * bb] --> bb carry : [pa * s * s] --> pa cond : [ya * bb] --> bb nil : [] --> bb sum : [pa * s * s] --> fa true : [] --> ya w : [] --> s We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): admit(X, nil) >? nil admit(X, !dot(Y, !dot(Z, !dot(w, U)))) >? cond(!870(sum(X, Y, Z), w), !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U))))) cond(true, X) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[admit(x_1, x_2)]] = admit(x_2, x_1) [[nil]] = _|_ We choose Lex = {admit} and Mul = {!870, !dot, carry, cond, sum, true, w}, and the following precedence: admit > !870 > !dot > cond > w > sum > carry = true Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: admit(X, _|_) >= _|_ admit(X, !dot(Y, !dot(Z, !dot(w, U)))) >= cond(!870(sum(X, Y, Z), w), !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U))))) cond(true, X) > X With these choices, we have: 1] admit(X, _|_) >= _|_ by (Bot) 2] admit(X, !dot(Y, !dot(Z, !dot(w, U)))) >= cond(!870(sum(X, Y, Z), w), !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U))))) because [3], by (Star) 3] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= cond(!870(sum(X, Y, Z), w), !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U))))) because admit > cond, [4] and [19], by (Copy) 4] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= !870(sum(X, Y, Z), w) because admit > !870, [5] and [18], by (Copy) 5] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= sum(X, Y, Z) because admit > sum, [6], [8] and [12], by (Copy) 6] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= X because [7], by (Select) 7] X >= X by (Meta) 8] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= Y because [9], by (Select) 9] !dot(Y, !dot(Z, !dot(w, U))) >= Y because [10], by (Star) 10] !dot*(Y, !dot(Z, !dot(w, U))) >= Y because [11], by (Select) 11] Y >= Y by (Meta) 12] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= Z because [13], by (Select) 13] !dot(Y, !dot(Z, !dot(w, U))) >= Z because [14], by (Star) 14] !dot*(Y, !dot(Z, !dot(w, U))) >= Z because [15], by (Select) 15] !dot(Z, !dot(w, U)) >= Z because [16], by (Star) 16] !dot*(Z, !dot(w, U)) >= Z because [17], by (Select) 17] Z >= Z by (Meta) 18] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= w because admit > w, by (Copy) 19] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= !dot(Y, !dot(Z, !dot(w, admit(carry(X, Y, Z), U)))) because admit > !dot, [8] and [20], by (Copy) 20] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= !dot(Z, !dot(w, admit(carry(X, Y, Z), U))) because admit > !dot, [12] and [21], by (Copy) 21] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= !dot(w, admit(carry(X, Y, Z), U)) because admit > !dot, [18] and [22], by (Copy) 22] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= admit(carry(X, Y, Z), U) because [23], [30] and [31], by (Stat) 23] !dot(Y, !dot(Z, !dot(w, U))) > U because [24], by definition 24] !dot*(Y, !dot(Z, !dot(w, U))) >= U because [25], by (Select) 25] !dot(Z, !dot(w, U)) >= U because [26], by (Star) 26] !dot*(Z, !dot(w, U)) >= U because [27], by (Select) 27] !dot(w, U) >= U because [28], by (Star) 28] !dot*(w, U) >= U because [29], by (Select) 29] U >= U by (Meta) 30] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= carry(X, Y, Z) because admit > carry, [6], [8] and [12], by (Copy) 31] admit*(X, !dot(Y, !dot(Z, !dot(w, U)))) >= U because [32], by (Select) 32] !dot(Y, !dot(Z, !dot(w, U))) >= U because [24], by (Star) 33] cond(true, X) > X because [34], by definition 34] cond*(true, X) >= X because [35], by (Select)
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