details

property	value
status	complete
benchmark	2.52.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.51025390625 seconds
cpu usage	0.507096863
max memory	2.0410368E7

stage attributes

key	value
output-size	17013
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. 0 : [] --> o f : [o * o * o] --> o s : [o] --> o f(X, 0, 0) => s(X) f(0, X, 0) => s(X) f(0, 0, X) => s(X) f(s(0), X, Y) => f(0, s(X), s(Y)) f(s(X), s(Y), 0) => f(X, Y, s(0)) f(s(X), 0, s(Y)) => f(X, s(0), Y) f(0, s(0), s(0)) => s(s(0)) f(s(X), s(Y), s(Z)) => f(X, Y, f(s(X), s(Y), Z)) f(0, s(s(X)), s(0)) => f(0, X, s(0)) f(0, s(0), s(s(X))) => f(0, s(0), X) f(0, s(s(X)), s(s(Y))) => f(0, X, f(0, s(s(X)), s(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]): f(X, 0, 0) >? s(X) f(0, X, 0) >? s(X) f(0, 0, X) >? s(X) f(s(0), X, Y) >? f(0, s(X), s(Y)) f(s(X), s(Y), 0) >? f(X, Y, s(0)) f(s(X), 0, s(Y)) >? f(X, s(0), Y) f(0, s(0), s(0)) >? s(s(0)) f(s(X), s(Y), s(Z)) >? f(X, Y, f(s(X), s(Y), Z)) f(0, s(s(X)), s(0)) >? f(0, X, s(0)) f(0, s(0), s(s(X))) >? f(0, s(0), X) f(0, s(s(X)), s(s(Y))) >? f(0, X, f(0, s(s(X)), s(Y))) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {f} and Mul = {0, s}, and the following precedence: f > s > 0 With these choices, we have: 1] f(X, 0, 0) >= s(X) because [2], by (Star) 2] f*(X, 0, 0) >= s(X) because f > s and [3], by (Copy) 3] f*(X, 0, 0) >= X because [4], by (Select) 4] X >= X by (Meta) 5] f(0, X, 0) > s(X) because [6], by definition 6] f*(0, X, 0) >= s(X) because f > s and [7], by (Copy) 7] f*(0, X, 0) >= X because [8], by (Select) 8] X >= X by (Meta) 9] f(0, 0, X) > s(X) because [10], by definition 10] f*(0, 0, X) >= s(X) because f > s and [11], by (Copy) 11] f*(0, 0, X) >= X because [12], by (Select) 12] X >= X by (Meta) 13] f(s(0), X, Y) >= f(0, s(X), s(Y)) because [14], by (Star) 14] f*(s(0), X, Y) >= f(0, s(X), s(Y)) because [15], [17], [18] and [20], by (Stat) 15] s(0) > 0 because [16], by definition 16] s*(0) >= 0 because s > 0, by (Copy) 17] f*(s(0), X, Y) >= 0 because f > 0, by (Copy) 18] f*(s(0), X, Y) >= s(X) because f > s and [19], by (Copy) 19] f*(s(0), X, Y) >= X because [8], by (Select) 20] f*(s(0), X, Y) >= s(Y) because f > s and [21], by (Copy) 21] f*(s(0), X, Y) >= Y because [12], by (Select) 22] f(s(X), s(Y), 0) >= f(X, Y, s(0)) because [23], by (Star) 23] f*(s(X), s(Y), 0) >= f(X, Y, s(0)) because [24], [26], [28] and [31], by (Stat) 24] s(X) > X because [25], by definition 25] s*(X) >= X because [4], by (Select) 26] f*(s(X), s(Y), 0) >= X because [27], by (Select) 27] s(X) >= X because [25], by (Star) 28] f*(s(X), s(Y), 0) >= Y because [29], by (Select) 29] s(Y) >= Y because [30], by (Star) 30] s*(Y) >= Y because [8], by (Select) 31] f*(s(X), s(Y), 0) >= s(0) because f > s and [32], by (Copy) 32] f*(s(X), s(Y), 0) >= 0 because f > 0, by (Copy) 33] f(s(X), 0, s(Y)) >= f(X, s(0), Y) because [34], by (Star) 34] f*(s(X), 0, s(Y)) >= f(X, s(0), Y) because [24], [35], [36] and [38], by (Stat) 35] f*(s(X), 0, s(Y)) >= X because [27], by (Select) 36] f*(s(X), 0, s(Y)) >= s(0) because f > s and [37], by (Copy) 37] f*(s(X), 0, s(Y)) >= 0 because f > 0, by (Copy) 38] f*(s(X), 0, s(Y)) >= Y because [39], by (Select) 39] s(Y) >= Y because [40], by (Star) 40] s*(Y) >= Y because [12], by (Select) 41] f(0, s(0), s(0)) >= s(s(0)) because [42], by (Star) 42] f*(0, s(0), s(0)) >= s(s(0)) because f > s and [43], by (Copy) 43] f*(0, s(0), s(0)) >= s(0) because [44], by (Select) popout

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all output return to TRS Stand 20472