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TRS Stand 20472 pair #381715825
details
property
value
status
complete
benchmark
Ex1_Luc02b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.116286993027 seconds
cpu usage
0.112900394
max memory
4902912.0
stage attributes
key
value
output-size
8478
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 activate : [o] --> o cons : [o * o] --> o first : [o * o] --> o from : [o] --> o n!6220!6220first : [o * o] --> o n!6220!6220from : [o] --> o nil : [] --> o s : [o] --> o sel : [o * o] --> o from(X) => cons(X, n!6220!6220from(s(X))) first(0, X) => nil first(s(X), cons(Y, Z)) => cons(Y, n!6220!6220first(X, activate(Z))) sel(0, cons(X, Y)) => X sel(s(X), cons(Y, Z)) => sel(X, activate(Z)) from(X) => n!6220!6220from(X) first(X, Y) => n!6220!6220first(X, Y) activate(n!6220!6220from(X)) => from(X) activate(n!6220!6220first(X, Y)) => first(X, Y) activate(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]): from(X) >? cons(X, n!6220!6220from(s(X))) first(0, X) >? nil first(s(X), cons(Y, Z)) >? cons(Y, n!6220!6220first(X, activate(Z))) sel(0, cons(X, Y)) >? X sel(s(X), cons(Y, Z)) >? sel(X, activate(Z)) from(X) >? n!6220!6220from(X) first(X, Y) >? n!6220!6220first(X, Y) activate(n!6220!6220from(X)) >? from(X) activate(n!6220!6220first(X, Y)) >? first(X, Y) activate(X) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[nil]] = _|_ We choose Lex = {sel} and Mul = {0, activate, cons, first, from, n!6220!6220first, n!6220!6220from, s}, and the following precedence: sel > activate = first = from > cons > n!6220!6220first > n!6220!6220from > 0 > s Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: from(X) > cons(X, n!6220!6220from(s(X))) first(0, X) >= _|_ first(s(X), cons(Y, Z)) >= cons(Y, n!6220!6220first(X, activate(Z))) sel(0, cons(X, Y)) >= X sel(s(X), cons(Y, Z)) > sel(X, activate(Z)) from(X) > n!6220!6220from(X) first(X, Y) > n!6220!6220first(X, Y) activate(n!6220!6220from(X)) >= from(X) activate(n!6220!6220first(X, Y)) >= first(X, Y) activate(X) >= X With these choices, we have: 1] from(X) > cons(X, n!6220!6220from(s(X))) because [2], by definition 2] from*(X) >= cons(X, n!6220!6220from(s(X))) because from > cons, [3] and [5], by (Copy) 3] from*(X) >= X because [4], by (Select) 4] X >= X by (Meta) 5] from*(X) >= n!6220!6220from(s(X)) because from > n!6220!6220from and [6], by (Copy) 6] from*(X) >= s(X) because from > s and [3], by (Copy) 7] first(0, X) >= _|_ by (Bot) 8] first(s(X), cons(Y, Z)) >= cons(Y, n!6220!6220first(X, activate(Z))) because [9], by (Star) 9] first*(s(X), cons(Y, Z)) >= cons(Y, n!6220!6220first(X, activate(Z))) because first > cons, [10] and [14], by (Copy) 10] first*(s(X), cons(Y, Z)) >= Y because [11], by (Select) 11] cons(Y, Z) >= Y because [12], by (Star) 12] cons*(Y, Z) >= Y because [13], by (Select) 13] Y >= Y by (Meta) 14] first*(s(X), cons(Y, Z)) >= n!6220!6220first(X, activate(Z)) because first > n!6220!6220first, [15] and [18], by (Copy) 15] first*(s(X), cons(Y, Z)) >= X because [16], by (Select) 16] s(X) >= X because [17], by (Star) 17] s*(X) >= X because [4], by (Select) 18] first*(s(X), cons(Y, Z)) >= activate(Z) because first = activate, first in Mul and [19], by (Stat) 19] cons(Y, Z) > Z because [20], by definition 20] cons*(Y, Z) >= Z because [21], by (Select) 21] Z >= Z by (Meta) 22] sel(0, cons(X, Y)) >= X because [23], by (Star) 23] sel*(0, cons(X, Y)) >= X because [24], by (Select) 24] cons(X, Y) >= X because [25], by (Star)
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