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TRS Stand 20472 pair #381714763
details
property
value
status
complete
benchmark
2.43.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.191380977631 seconds
cpu usage
0.187844915
max memory
9302016.0
stage attributes
key
value
output-size
8553
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. !770 : [o * o] --> o !dot : [o * o] --> o !plus!plus : [o * o] --> o false : [] --> o if : [o * o * o] --> o merge : [o * o] --> o nil : [] --> o true : [] --> o merge(nil, X) => X merge(X, nil) => X merge(!dot(X, Y), !dot(Z, U)) => if(!770(X, Z), !dot(X, merge(Y, !dot(Z, U))), !dot(Z, merge(!dot(X, Y), U))) !plus!plus(nil, X) => X !plus!plus(!dot(X, Y), Z) => !dot(X, !plus!plus(Y, Z)) if(true, X, Y) => X if(false, X, Y) => 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]): merge(nil, X) >? X merge(X, nil) >? X merge(!dot(X, Y), !dot(Z, U)) >? if(!770(X, Z), !dot(X, merge(Y, !dot(Z, U))), !dot(Z, merge(!dot(X, Y), U))) !plus!plus(nil, X) >? X !plus!plus(!dot(X, Y), Z) >? !dot(X, !plus!plus(Y, Z)) if(true, X, Y) >? X if(false, X, Y) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {} and Mul = {!770, !dot, !plus!plus, false, if, merge, nil, true}, and the following precedence: !plus!plus > !770 = merge > !dot > nil > true > false > if With these choices, we have: 1] merge(nil, X) >= X because [2], by (Star) 2] merge*(nil, X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] merge(X, nil) > X because [5], by definition 5] merge*(X, nil) >= X because [6], by (Select) 6] X >= X by (Meta) 7] merge(!dot(X, Y), !dot(Z, U)) >= if(!770(X, Z), !dot(X, merge(Y, !dot(Z, U))), !dot(Z, merge(!dot(X, Y), U))) because [8], by (Star) 8] merge*(!dot(X, Y), !dot(Z, U)) >= if(!770(X, Z), !dot(X, merge(Y, !dot(Z, U))), !dot(Z, merge(!dot(X, Y), U))) because merge > if, [9], [15] and [23], by (Copy) 9] merge*(!dot(X, Y), !dot(Z, U)) >= !770(X, Z) because merge = !770, merge in Mul, [10] and [12], by (Stat) 10] !dot(X, Y) >= X because [11], by (Star) 11] !dot*(X, Y) >= X because [6], by (Select) 12] !dot(Z, U) > Z because [13], by definition 13] !dot*(Z, U) >= Z because [14], by (Select) 14] Z >= Z by (Meta) 15] merge*(!dot(X, Y), !dot(Z, U)) >= !dot(X, merge(Y, !dot(Z, U))) because merge > !dot, [16] and [17], by (Copy) 16] merge*(!dot(X, Y), !dot(Z, U)) >= X because [10], by (Select) 17] merge*(!dot(X, Y), !dot(Z, U)) >= merge(Y, !dot(Z, U)) because merge in Mul, [18] and [20], by (Stat) 18] !dot(X, Y) > Y because [19], by definition 19] !dot*(X, Y) >= Y because [3], by (Select) 20] !dot(Z, U) >= !dot(Z, U) because !dot in Mul, [21] and [22], by (Fun) 21] Z >= Z by (Meta) 22] U >= U by (Meta) 23] merge*(!dot(X, Y), !dot(Z, U)) >= !dot(Z, merge(!dot(X, Y), U)) because merge > !dot, [24] and [26], by (Copy) 24] merge*(!dot(X, Y), !dot(Z, U)) >= Z because [25], by (Select) 25] !dot(Z, U) >= Z because [13], by (Star) 26] merge*(!dot(X, Y), !dot(Z, U)) >= merge(!dot(X, Y), U) because merge in Mul, [27] and [30], by (Stat) 27] !dot(X, Y) >= !dot(X, Y) because !dot in Mul, [28] and [29], by (Fun) 28] X >= X by (Meta) 29] Y >= Y by (Meta) 30] !dot(Z, U) > U because [31], by definition 31] !dot*(Z, U) >= U because [22], by (Select) 32] !plus!plus(nil, X) >= X because [33], by (Star) 33] !plus!plus*(nil, X) >= X because [29], by (Select) 34] !plus!plus(!dot(X, Y), Z) > !dot(X, !plus!plus(Y, Z)) because [35], by definition 35] !plus!plus*(!dot(X, Y), Z) >= !dot(X, !plus!plus(Y, Z)) because !plus!plus > !dot, [36] and [37], by (Copy) 36] !plus!plus*(!dot(X, Y), Z) >= X because [10], by (Select) 37] !plus!plus*(!dot(X, Y), Z) >= !plus!plus(Y, Z) because !plus!plus in Mul, [18] and [38], by (Stat) 38] Z >= Z by (Meta) 39] if(true, X, Y) >= X because [40], by (Star) 40] if*(true, X, Y) >= X because [28], by (Select) 41] if(false, X, Y) >= X because [42], by (Star) 42] if*(false, X, Y) >= X because [28], by (Select) We can thus remove the following rules: merge(X, nil) => X
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