details

property	value
status	complete
benchmark	4.05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n104.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0718059539795 seconds
cpu usage	0.068280946
max memory	3366912.0

stage attributes

key	value
output-size	4980
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 1 : [] --> o !times(X, !plus(Y, Z)) => !plus(!times(X, Y), !times(X, Z)) !times(!plus(X, Y), Z) => !plus(!times(X, Z), !times(Y, Z)) !times(X, 1) => X !times(1, X) => X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): !times(X, !plus(Y, Z)) >? !plus(!times(X, Y), !times(X, Z)) !times(!plus(X, Y), Z) >? !plus(!times(X, Z), !times(Y, Z)) !times(X, 1) >? X !times(1, X) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {} and Mul = {!plus, !times, 1}, and the following precedence: !times > !plus > 1 With these choices, we have: 1] !times(X, !plus(Y, Z)) >= !plus(!times(X, Y), !times(X, Z)) because [2], by (Star) 2] !times*(X, !plus(Y, Z)) >= !plus(!times(X, Y), !times(X, Z)) because !times > !plus, [3] and [8], by (Copy) 3] !times*(X, !plus(Y, Z)) >= !times(X, Y) because !times in Mul, [4] and [5], by (Stat) 4] X >= X by (Meta) 5] !plus(Y, Z) > Y because [6], by definition 6] !plus*(Y, Z) >= Y because [7], by (Select) 7] Y >= Y by (Meta) 8] !times*(X, !plus(Y, Z)) >= !times(X, Z) because !times in Mul, [4] and [9], by (Stat) 9] !plus(Y, Z) > Z because [10], by definition 10] !plus*(Y, Z) >= Z because [11], by (Select) 11] Z >= Z by (Meta) 12] !times(!plus(X, Y), Z) > !plus(!times(X, Z), !times(Y, Z)) because [13], by definition 13] !times*(!plus(X, Y), Z) >= !plus(!times(X, Z), !times(Y, Z)) because !times > !plus, [14] and [18], by (Copy) 14] !times*(!plus(X, Y), Z) >= !times(X, Z) because !times in Mul, [15] and [17], by (Stat) 15] !plus(X, Y) > X because [16], by definition 16] !plus*(X, Y) >= X because [4], by (Select) 17] Z >= Z by (Meta) 18] !times*(!plus(X, Y), Z) >= !times(Y, Z) because !times in Mul, [19] and [17], by (Stat) 19] !plus(X, Y) > Y because [20], by definition 20] !plus*(X, Y) >= Y because [7], by (Select) 21] !times(X, 1) >= X because [22], by (Star) 22] !times*(X, 1) >= X because [4], by (Select) 23] !times(1, X) >= X because [24], by (Star) 24] !times*(1, X) >= X because [7], by (Select) We can thus remove the following rules: !times(!plus(X, Y), Z) => !plus(!times(X, Z), !times(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]): !times(X, !plus(Y, Z)) >? !plus(!times(X, Y), !times(X, Z)) !times(X, 1) >? X !times(1, X) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {} and Mul = {!plus, !times, 1}, and the following precedence: !times > !plus > 1 With these choices, we have: 1] !times(X, !plus(Y, Z)) > !plus(!times(X, Y), !times(X, Z)) because [2], by definition 2] !times*(X, !plus(Y, Z)) >= !plus(!times(X, Y), !times(X, Z)) because !times > !plus, [3] and [8], by (Copy) 3] !times*(X, !plus(Y, Z)) >= !times(X, Y) because !times in Mul, [4] and [5], by (Stat) 4] X >= X by (Meta) 5] !plus(Y, Z) > Y because [6], by definition 6] !plus*(Y, Z) >= Y because [7], by (Select) 7] Y >= Y by (Meta) 8] !times*(X, !plus(Y, Z)) >= !times(X, Z) because !times in Mul, [4] and [9], by (Stat) 9] !plus(Y, Z) > Z because [10], by definition 10] !plus*(Y, Z) >= Z because [11], by (Select) 11] Z >= Z by (Meta) 12] !times(X, 1) > X because [13], by definition 13] !times*(X, 1) >= X because [4], by (Select) popout

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