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TRS Stand 20472 pair #381712137
details
property
value
status
complete
benchmark
list-sum-prod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.819221019745 seconds
cpu usage
0.100205996
max memory
4952064.0
stage attributes
key
value
output-size
6357
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. !plus : [o * o] --> o !times : [o * o] --> o 0 : [] --> o cons : [o * o] --> o nil : [] --> o prod : [o] --> o s : [o] --> o sum : [o] --> o !plus(X, 0) => X !plus(0, X) => X !plus(s(X), s(Y)) => s(s(!plus(X, Y))) !times(X, 0) => 0 !times(0, X) => 0 !times(s(X), s(Y)) => s(!plus(!times(X, Y), !plus(X, Y))) sum(nil) => 0 sum(cons(X, Y)) => !plus(X, sum(Y)) prod(nil) => s(0) prod(cons(X, Y)) => !times(X, prod(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]): !plus(X, 0) >? X !plus(0, X) >? X !plus(s(X), s(Y)) >? s(s(!plus(X, Y))) !times(X, 0) >? 0 !times(0, X) >? 0 !times(s(X), s(Y)) >? s(!plus(!times(X, Y), !plus(X, Y))) sum(nil) >? 0 sum(cons(X, Y)) >? !plus(X, sum(Y)) prod(nil) >? s(0) prod(cons(X, Y)) >? !times(X, prod(Y)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[0]] = _|_ We choose Lex = {} and Mul = {!plus, !times, cons, nil, prod, s, sum}, and the following precedence: cons > !times > nil > sum > !plus > prod > s Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: !plus(X, _|_) > X !plus(_|_, X) > X !plus(s(X), s(Y)) > s(s(!plus(X, Y))) !times(X, _|_) >= _|_ !times(_|_, X) >= _|_ !times(s(X), s(Y)) > s(!plus(!times(X, Y), !plus(X, Y))) sum(nil) >= _|_ sum(cons(X, Y)) >= !plus(X, sum(Y)) prod(nil) > s(_|_) prod(cons(X, Y)) >= !times(X, prod(Y)) With these choices, we have: 1] !plus(X, _|_) > X because [2], by definition 2] !plus*(X, _|_) >= X because [3], by (Select) 3] X >= X by (Meta) 4] !plus(_|_, X) > X because [5], by definition 5] !plus*(_|_, X) >= X because [3], by (Select) 6] !plus(s(X), s(Y)) > s(s(!plus(X, Y))) because [7], by definition 7] !plus*(s(X), s(Y)) >= s(s(!plus(X, Y))) because !plus > s and [8], by (Copy) 8] !plus*(s(X), s(Y)) >= s(!plus(X, Y)) because !plus > s and [9], by (Copy) 9] !plus*(s(X), s(Y)) >= !plus(X, Y) because !plus in Mul, [10] and [12], by (Stat) 10] s(X) >= X because [11], by (Star) 11] s*(X) >= X because [3], by (Select) 12] s(Y) > Y because [13], by definition 13] s*(Y) >= Y because [14], by (Select) 14] Y >= Y by (Meta) 15] !times(X, _|_) >= _|_ by (Bot) 16] !times(_|_, X) >= _|_ by (Bot) 17] !times(s(X), s(Y)) > s(!plus(!times(X, Y), !plus(X, Y))) because [18], by definition 18] !times*(s(X), s(Y)) >= s(!plus(!times(X, Y), !plus(X, Y))) because !times > s and [19], by (Copy) 19] !times*(s(X), s(Y)) >= !plus(!times(X, Y), !plus(X, Y)) because !times > !plus, [20] and [24], by (Copy) 20] !times*(s(X), s(Y)) >= !times(X, Y) because !times in Mul, [21] and [23], by (Stat) 21] s(X) > X because [22], by definition 22] s*(X) >= X because [3], by (Select) 23] s(Y) >= Y because [13], by (Star) 24] !times*(s(X), s(Y)) >= !plus(X, Y) because !times > !plus, [25] and [26], by (Copy)
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