details

property	value
status	complete
benchmark	2.08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n108.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.119003772736 seconds
cpu usage	0.108365257
max memory	4706304.0

stage attributes

key	value
output-size	6639
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 a : [] --> o b : [] --> o f : [o * o] --> o !plus(a, b) => !plus(b, a) !plus(a, !plus(b, X)) => !plus(b, !plus(a, X)) !plus(!plus(X, Y), Z) => !plus(X, !plus(Y, Z)) f(a, X) => a f(b, X) => b f(!plus(X, Y), Z) => !plus(f(X, Z), f(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]): !plus(a, b) >? !plus(b, a) !plus(a, !plus(b, X)) >? !plus(b, !plus(a, X)) !plus(!plus(X, Y), Z) >? !plus(X, !plus(Y, Z)) f(a, X) >? a f(b, X) >? b f(!plus(X, Y), Z) >? !plus(f(X, Z), f(Y, Z)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {!plus} and Mul = {a, b, f}, and the following precedence: f > !plus > a > b With these choices, we have: 1] !plus(a, b) >= !plus(b, a) because [2], by (Star) 2] !plus*(a, b) >= !plus(b, a) because [3], [5] and [6], by (Stat) 3] a > b because [4], by definition 4] a* >= b because a > b, by (Copy) 5] !plus*(a, b) >= b because !plus > b, by (Copy) 6] !plus*(a, b) >= a because !plus > a, by (Copy) 7] !plus(a, !plus(b, X)) > !plus(b, !plus(a, X)) because [8], by definition 8] !plus*(a, !plus(b, X)) >= !plus(b, !plus(a, X)) because [3], [9] and [10], by (Stat) 9] !plus*(a, !plus(b, X)) >= b because !plus > b, by (Copy) 10] !plus*(a, !plus(b, X)) >= !plus(a, X) because [11], [12], [15] and [16], by (Stat) 11] a >= a by (Fun) 12] !plus(b, X) > X because [13], by definition 13] !plus*(b, X) >= X because [14], by (Select) 14] X >= X by (Meta) 15] !plus*(a, !plus(b, X)) >= a because !plus > a, by (Copy) 16] !plus*(a, !plus(b, X)) >= X because [17], by (Select) 17] !plus(b, X) >= X because [13], by (Star) 18] !plus(!plus(X, Y), Z) > !plus(X, !plus(Y, Z)) because [19], by definition 19] !plus*(!plus(X, Y), Z) >= !plus(X, !plus(Y, Z)) because [20], [23] and [25], by (Stat) 20] !plus(X, Y) > X because [21], by definition 21] !plus*(X, Y) >= X because [22], by (Select) 22] X >= X by (Meta) 23] !plus*(!plus(X, Y), Z) >= X because [24], by (Select) 24] !plus(X, Y) >= X because [21], by (Star) 25] !plus*(!plus(X, Y), Z) >= !plus(Y, Z) because [26], [29] and [31], by (Stat) 26] !plus(X, Y) > Y because [27], by definition 27] !plus*(X, Y) >= Y because [28], by (Select) 28] Y >= Y by (Meta) 29] !plus*(!plus(X, Y), Z) >= Y because [30], by (Select) 30] !plus(X, Y) >= Y because [27], by (Star) 31] !plus*(!plus(X, Y), Z) >= Z because [14], by (Select) 32] f(a, X) >= a because [33], by (Star) 33] f*(a, X) >= a because f > a, by (Copy) 34] f(b, X) >= b because [35], by (Star) 35] f*(b, X) >= b because f > b, by (Copy) 36] f(!plus(X, Y), Z) >= !plus(f(X, Z), f(Y, Z)) because [37], by (Star) 37] f*(!plus(X, Y), Z) >= !plus(f(X, Z), f(Y, Z)) because f > !plus, [38] and [40], by (Copy) 38] f*(!plus(X, Y), Z) >= f(X, Z) because f in Mul, [20] and [39], by (Stat) 39] Z >= Z by (Meta) 40] f*(!plus(X, Y), Z) >= f(Y, Z) because f in Mul, [26] and [39], by (Stat) We can thus remove the following rules: !plus(a, !plus(b, X)) => !plus(b, !plus(a, X)) !plus(!plus(X, Y), Z) => !plus(X, !plus(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]): !plus(a, b) >? !plus(b, a) f(a, X) >? a f(b, X) >? b popout

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