details

property	value
status	complete
benchmark	30.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n111.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0756900310516 seconds
cpu usage	0.071986591
max memory	4386816.0

stage attributes

key	value
output-size	3926
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. !colon : [o * o] --> o C : [] --> o !colon(!colon(!colon(!colon(C, X), Y), Z), U) => !colon(!colon(X, Z), !colon(!colon(!colon(X, Y), Z), U)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): !colon(!colon(!colon(!colon(C, X), Y), Z), U) >? !colon(!colon(X, Z), !colon(!colon(!colon(X, Y), Z), U)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {!colon} and Mul = {C}, and the following precedence: !colon > C With these choices, we have: 1] !colon(!colon(!colon(!colon(C, X), Y), Z), U) > !colon(!colon(X, Z), !colon(!colon(!colon(X, Y), Z), U)) because [2], by definition 2] !colon*(!colon(!colon(!colon(C, X), Y), Z), U) >= !colon(!colon(X, Z), !colon(!colon(!colon(X, Y), Z), U)) because [3], [14] and [18], by (Stat) 3] !colon(!colon(!colon(C, X), Y), Z) > !colon(X, Z) because [4], by definition 4] !colon*(!colon(!colon(C, X), Y), Z) >= !colon(X, Z) because [5], [10] and [12], by (Stat) 5] !colon(!colon(C, X), Y) > X because [6], by definition 6] !colon*(!colon(C, X), Y) >= X because [7], by (Select) 7] !colon(C, X) >= X because [8], by (Star) 8] !colon*(C, X) >= X because [9], by (Select) 9] X >= X by (Meta) 10] !colon*(!colon(!colon(C, X), Y), Z) >= X because [11], by (Select) 11] !colon(!colon(C, X), Y) >= X because [6], by (Star) 12] !colon*(!colon(!colon(C, X), Y), Z) >= Z because [13], by (Select) 13] Z >= Z by (Meta) 14] !colon*(!colon(!colon(!colon(C, X), Y), Z), U) >= !colon(X, Z) because [15], by (Select) 15] !colon(!colon(!colon(C, X), Y), Z) >= !colon(X, Z) because [16] and [17], by (Fun) 16] !colon(!colon(C, X), Y) >= X because [6], by (Star) 17] Z >= Z by (Meta) 18] !colon*(!colon(!colon(!colon(C, X), Y), Z), U) >= !colon(!colon(!colon(X, Y), Z), U) because [19], [31] and [34], by (Stat) 19] !colon(!colon(!colon(C, X), Y), Z) > !colon(!colon(X, Y), Z) because [20], by definition 20] !colon*(!colon(!colon(C, X), Y), Z) >= !colon(!colon(X, Y), Z) because [21], [27] and [12], by (Stat) 21] !colon(!colon(C, X), Y) > !colon(X, Y) because [22], by definition 22] !colon*(!colon(C, X), Y) >= !colon(X, Y) because [23], [6] and [25], by (Stat) 23] !colon(C, X) > X because [24], by definition 24] !colon*(C, X) >= X because [9], by (Select) 25] !colon*(!colon(C, X), Y) >= Y because [26], by (Select) 26] Y >= Y by (Meta) 27] !colon*(!colon(!colon(C, X), Y), Z) >= !colon(X, Y) because [28], by (Select) 28] !colon(!colon(C, X), Y) >= !colon(X, Y) because [29] and [30], by (Fun) 29] !colon(C, X) >= X because [24], by (Star) 30] Y >= Y by (Meta) 31] !colon*(!colon(!colon(!colon(C, X), Y), Z), U) >= !colon(!colon(X, Y), Z) because [32], by (Select) 32] !colon(!colon(!colon(C, X), Y), Z) >= !colon(!colon(X, Y), Z) because [33] and [17], by (Fun) 33] !colon(!colon(C, X), Y) >= !colon(X, Y) because [29] and [30], by (Fun) 34] !colon*(!colon(!colon(!colon(C, X), Y), Z), U) >= U because [35], by (Select) 35] U >= U by (Meta) We can thus remove the following rules: !colon(!colon(!colon(!colon(C, X), Y), Z), U) => !colon(!colon(X, Z), !colon(!colon(!colon(X, Y), Z), U)) All rules were succesfully removed. Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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