Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
HRS union beta 16688 pair #381734293
details
property
value
status
complete
benchmark
06plusmult.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Blanqui_15
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
1.28894901276 seconds
cpu usage
0.167354024
max memory
6201344.0
stage attributes
key
value
output-size
10444
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: mult : [N * N] --> N plus : [N * N] --> N s : [N] --> N z : [] --> N Rules: plus(z, x) => x plus(s(x), y) => plus(x, s(y)) plus(plus(x, y), u) => plus(x, plus(y, u)) mult(z, x) => z mult(s(x), y) => plus(mult(x, y), y) mult(plus(x, y), u) => plus(mult(x, u), mult(y, u)) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): plus(z, X) >? X plus(s(X), Y) >? plus(X, s(Y)) plus(plus(X, Y), Z) >? plus(X, plus(Y, Z)) mult(z, X) >? z mult(s(X), Y) >? plus(mult(X, Y), Y) mult(plus(X, Y), Z) >? plus(mult(X, Z), mult(Y, Z)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[z]] = _|_ We choose Lex = {plus} and Mul = {mult, s}, and the following precedence: mult > plus > s Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: plus(_|_, X) >= X plus(s(X), Y) >= plus(X, s(Y)) plus(plus(X, Y), Z) > plus(X, plus(Y, Z)) mult(_|_, X) >= _|_ mult(s(X), Y) >= plus(mult(X, Y), Y) mult(plus(X, Y), Z) > plus(mult(X, Z), mult(Y, Z)) With these choices, we have: 1] plus(_|_, X) >= X because [2], by (Star) 2] plus*(_|_, X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] plus(s(X), Y) >= plus(X, s(Y)) because [5], by (Star) 5] plus*(s(X), Y) >= plus(X, s(Y)) because [6], [9] and [11], by (Stat) 6] s(X) > X because [7], by definition 7] s*(X) >= X because [8], by (Select) 8] X >= X by (Meta) 9] plus*(s(X), Y) >= X because [10], by (Select) 10] s(X) >= X because [7], by (Star) 11] plus*(s(X), Y) >= s(Y) because plus > s and [12], by (Copy) 12] plus*(s(X), Y) >= Y because [13], by (Select) 13] Y >= Y by (Meta) 14] plus(plus(X, Y), Z) > plus(X, plus(Y, Z)) because [15], by definition 15] plus*(plus(X, Y), Z) >= plus(X, plus(Y, Z)) because [16], [19] and [21], by (Stat) 16] plus(X, Y) > X because [17], by definition 17] plus*(X, Y) >= X because [18], by (Select) 18] X >= X by (Meta) 19] plus*(plus(X, Y), Z) >= X because [20], by (Select) 20] plus(X, Y) >= X because [17], by (Star) 21] plus*(plus(X, Y), Z) >= plus(Y, Z) because [22], [25] and [27], by (Stat) 22] plus(X, Y) > Y because [23], by definition 23] plus*(X, Y) >= Y because [24], by (Select) 24] Y >= Y by (Meta) 25] plus*(plus(X, Y), Z) >= Y because [26], by (Select) 26] plus(X, Y) >= Y because [23], by (Star) 27] plus*(plus(X, Y), Z) >= Z because [28], by (Select) 28] Z >= Z by (Meta) 29] mult(_|_, X) >= _|_ by (Bot) 30] mult(s(X), Y) >= plus(mult(X, Y), Y) because [31], by (Star) 31] mult*(s(X), Y) >= plus(mult(X, Y), Y) because mult > plus, [32] and [37], by (Copy) 32] mult*(s(X), Y) >= mult(X, Y) because mult in Mul, [33] and [36], by (Stat) 33] s(X) > X because [34], by definition 34] s*(X) >= X because [35], by (Select) 35] X >= X by (Meta) 36] Y >= Y by (Meta) 37] mult*(s(X), Y) >= Y because [36], by (Select)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to HRS union beta 16688