Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381710071
details
property
value
status
complete
benchmark
12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.220664978027 seconds
cpu usage
0.217346806
max memory
9019392.0
stage attributes
key
value
output-size
10868
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. and : [o * o] --> o not : [o] --> o or : [o * o] --> o not(not(X)) => X not(or(X, Y)) => and(not(X), not(Y)) not(and(X, Y)) => or(not(X), not(Y)) and(X, or(Y, Z)) => or(and(X, Y), and(X, Z)) and(or(X, Y), Z) => or(and(Z, X), and(Z, Y)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): not(not(X)) >? X not(or(X, Y)) >? and(not(X), not(Y)) not(and(X, Y)) >? or(not(X), not(Y)) and(X, or(Y, Z)) >? or(and(X, Y), and(X, Z)) and(or(X, Y), Z) >? or(and(Z, X), and(Z, Y)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {not} and Mul = {and, or}, and the following precedence: not > and > or With these choices, we have: 1] not(not(X)) >= X because [2], by (Star) 2] not*(not(X)) >= X because [3], by (Select) 3] not(X) >= X because [4], by (Star) 4] not*(X) >= X because [5], by (Select) 5] X >= X by (Meta) 6] not(or(X, Y)) >= and(not(X), not(Y)) because [7], by (Star) 7] not*(or(X, Y)) >= and(not(X), not(Y)) because not > and, [8] and [13], by (Copy) 8] not*(or(X, Y)) >= not(X) because [9] and [11], by (Stat) 9] or(X, Y) > X because [10], by definition 10] or*(X, Y) >= X because [5], by (Select) 11] not*(or(X, Y)) >= X because [12], by (Select) 12] or(X, Y) >= X because [10], by (Star) 13] not*(or(X, Y)) >= not(Y) because [14] and [17], by (Stat) 14] or(X, Y) > Y because [15], by definition 15] or*(X, Y) >= Y because [16], by (Select) 16] Y >= Y by (Meta) 17] not*(or(X, Y)) >= Y because [18], by (Select) 18] or(X, Y) >= Y because [15], by (Star) 19] not(and(X, Y)) > or(not(X), not(Y)) because [20], by definition 20] not*(and(X, Y)) >= or(not(X), not(Y)) because not > or, [21] and [26], by (Copy) 21] not*(and(X, Y)) >= not(X) because [22] and [24], by (Stat) 22] and(X, Y) > X because [23], by definition 23] and*(X, Y) >= X because [5], by (Select) 24] not*(and(X, Y)) >= X because [25], by (Select) 25] and(X, Y) >= X because [23], by (Star) 26] not*(and(X, Y)) >= not(Y) because [27] and [29], by (Stat) 27] and(X, Y) > Y because [28], by definition 28] and*(X, Y) >= Y because [16], by (Select) 29] not*(and(X, Y)) >= Y because [30], by (Select) 30] and(X, Y) >= Y because [28], by (Star) 31] and(X, or(Y, Z)) >= or(and(X, Y), and(X, Z)) because [32], by (Star) 32] and*(X, or(Y, Z)) >= or(and(X, Y), and(X, Z)) because and > or, [33] and [37], by (Copy) 33] and*(X, or(Y, Z)) >= and(X, Y) because and in Mul, [34] and [35], by (Stat) 34] X >= X by (Meta) 35] or(Y, Z) > Y because [36], by definition 36] or*(Y, Z) >= Y because [16], by (Select) 37] and*(X, or(Y, Z)) >= and(X, Z) because and in Mul, [34] and [38], by (Stat) 38] or(Y, Z) > Z because [39], by definition 39] or*(Y, Z) >= Z because [40], by (Select) 40] Z >= Z by (Meta) 41] and(or(X, Y), Z) >= or(and(Z, X), and(Z, Y)) because [42], by (Star) 42] and*(or(X, Y), Z) >= or(and(Z, X), and(Z, Y)) because and > or, [43] and [44], by (Copy) 43] and*(or(X, Y), Z) >= and(Z, X) because and in Mul, [35] and [34], by (Stat) 44] and*(or(X, Y), Z) >= and(Z, Y) because and in Mul, [38] and [34], by (Stat) We can thus remove the following rules: not(and(X, Y)) => or(not(X), not(Y)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): not(not(X)) >? X not(or(X, Y)) >? and(not(X), not(Y)) and(X, or(Y, Z)) >? or(and(X, Y), and(X, Z)) and(or(X, Y), Z) >? or(and(Z, X), and(Z, Y))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472