details

property	value
status	complete
benchmark	2.23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.315245866776 seconds
cpu usage	0.281207296
max memory	9302016.0

stage attributes

key	value
output-size	15777
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !plus : [o * o] --> o !times : [o * o] --> o 0 : [] --> o 1 : [] --> o fac : [o] --> o floop : [o * o] --> o s : [o] --> o fac(0) => 1 fac(s(X)) => !times(s(X), fac(X)) floop(0, X) => X floop(s(X), Y) => floop(X, !times(s(X), Y)) !times(X, 0) => 0 !times(X, s(Y)) => !plus(!times(X, Y), X) !plus(X, 0) => X !plus(X, s(Y)) => s(!plus(X, Y)) 1 => s(0) fac(0) => s(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]): fac(0) >? 1 fac(s(X)) >? !times(s(X), fac(X)) floop(0, X) >? X floop(s(X), Y) >? floop(X, !times(s(X), Y)) !times(X, 0) >? 0 !times(X, s(Y)) >? !plus(!times(X, Y), X) !plus(X, 0) >? X !plus(X, s(Y)) >? s(!plus(X, Y)) 1 >? s(0) fac(0) >? s(0) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[0]] = _|_ We choose Lex = {floop} and Mul = {!plus, !times, 1, fac, s}, and the following precedence: fac > 1 > floop > !times > !plus > s Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: fac(_|_) >= 1 fac(s(X)) >= !times(s(X), fac(X)) floop(_|_, X) >= X floop(s(X), Y) >= floop(X, !times(s(X), Y)) !times(X, _|_) >= _|_ !times(X, s(Y)) > !plus(!times(X, Y), X) !plus(X, _|_) >= X !plus(X, s(Y)) >= s(!plus(X, Y)) 1 >= s(_|_) fac(_|_) >= s(_|_) With these choices, we have: 1] fac(_|_) >= 1 because [2], by (Star) 2] fac*(_|_) >= 1 because fac > 1, by (Copy) 3] fac(s(X)) >= !times(s(X), fac(X)) because [4], by (Star) 4] fac*(s(X)) >= !times(s(X), fac(X)) because fac > !times, [5] and [8], by (Copy) 5] fac*(s(X)) >= s(X) because [6], by (Select) 6] s(X) >= s(X) because s in Mul and [7], by (Fun) 7] X >= X by (Meta) 8] fac*(s(X)) >= fac(X) because fac in Mul and [9], by (Stat) 9] s(X) > X because [10], by definition 10] s*(X) >= X because [7], by (Select) 11] floop(_|_, X) >= X because [12], by (Star) 12] floop*(_|_, X) >= X because [13], by (Select) 13] X >= X by (Meta) 14] floop(s(X), Y) >= floop(X, !times(s(X), Y)) because [15], by (Star) 15] floop*(s(X), Y) >= floop(X, !times(s(X), Y)) because [9], [16] and [18], by (Stat) 16] floop*(s(X), Y) >= X because [17], by (Select) 17] s(X) >= X because [10], by (Star) 18] floop*(s(X), Y) >= !times(s(X), Y) because floop > !times, [19] and [20], by (Copy) 19] floop*(s(X), Y) >= s(X) because floop > s and [16], by (Copy) 20] floop*(s(X), Y) >= Y because [13], by (Select) 21] !times(X, _|_) >= _|_ by (Bot) 22] !times(X, s(Y)) > !plus(!times(X, Y), X) because [23], by definition 23] !times*(X, s(Y)) >= !plus(!times(X, Y), X) because !times > !plus, [24] and [27], by (Copy) 24] !times*(X, s(Y)) >= !times(X, Y) because !times in Mul, [7] and [25], by (Stat) 25] s(Y) > Y because [26], by definition popout

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