details

property	value
status	complete
benchmark	4.20.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.301085948944 seconds
cpu usage	0.297761918
max memory	1.1628544E7

stage attributes

key	value
output-size	18262
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 false : [] --> o implies : [o * o] --> o not : [o] --> o or : [o * o] --> o true : [] --> o xor : [o * o] --> o not(X) => xor(X, true) or(X, Y) => xor(and(X, Y), xor(X, Y)) implies(X, Y) => xor(and(X, Y), xor(X, true)) and(X, true) => X and(X, false) => false and(X, X) => X xor(X, false) => X xor(X, X) => false and(xor(X, Y), Z) => xor(and(X, Z), and(Y, Z)) 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(X) >? xor(X, true) or(X, Y) >? xor(and(X, Y), xor(X, Y)) implies(X, Y) >? xor(and(X, Y), xor(X, true)) and(X, true) >? X and(X, false) >? false and(X, X) >? X xor(X, false) >? X xor(X, X) >? false and(xor(X, Y), Z) >? xor(and(X, Z), and(Y, Z)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[false]] = _|_ [[true]] = _|_ We choose Lex = {} and Mul = {and, implies, not, or, xor}, and the following precedence: or > implies > and > not > xor Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: not(X) >= xor(X, _|_) or(X, Y) >= xor(and(X, Y), xor(X, Y)) implies(X, Y) >= xor(and(X, Y), xor(X, _|_)) and(X, _|_) >= X and(X, _|_) >= _|_ and(X, X) > X xor(X, _|_) > X xor(X, X) >= _|_ and(xor(X, Y), Z) >= xor(and(X, Z), and(Y, Z)) With these choices, we have: 1] not(X) >= xor(X, _|_) because [2], by (Star) 2] not*(X) >= xor(X, _|_) because not > xor, [3] and [5], by (Copy) 3] not*(X) >= X because [4], by (Select) 4] X >= X by (Meta) 5] not*(X) >= _|_ by (Bot) 6] or(X, Y) >= xor(and(X, Y), xor(X, Y)) because [7], by (Star) 7] or*(X, Y) >= xor(and(X, Y), xor(X, Y)) because or > xor, [8] and [12], by (Copy) 8] or*(X, Y) >= and(X, Y) because or > and, [9] and [10], by (Copy) 9] or*(X, Y) >= X because [4], by (Select) 10] or*(X, Y) >= Y because [11], by (Select) 11] Y >= Y by (Meta) 12] or*(X, Y) >= xor(X, Y) because or > xor, [9] and [10], by (Copy) 13] implies(X, Y) >= xor(and(X, Y), xor(X, _|_)) because [14], by (Star) 14] implies*(X, Y) >= xor(and(X, Y), xor(X, _|_)) because implies > xor, [15] and [18], by (Copy) 15] implies*(X, Y) >= and(X, Y) because implies > and, [16] and [17], by (Copy) 16] implies*(X, Y) >= X because [4], by (Select) 17] implies*(X, Y) >= Y because [11], by (Select) 18] implies*(X, Y) >= xor(X, _|_) because implies > xor, [16] and [19], by (Copy) 19] implies*(X, Y) >= _|_ by (Bot) 20] and(X, _|_) >= X because [21], by (Star) 21] and*(X, _|_) >= X because [4], by (Select) 22] and(X, _|_) >= _|_ by (Bot) 23] and(X, X) > X because [24], by definition 24] and*(X, X) >= X because [4], by (Select) 25] xor(X, _|_) > X because [26], by definition 26] xor*(X, _|_) >= X because [4], by (Select) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Stand 20472