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TRS Stand 20472 pair #381713776
details
property
value
status
complete
benchmark
Ex1_2_AEL03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n021.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.317182064056 seconds
cpu usage
0.29816954
max memory
1.4307328E7
stage attributes
key
value
output-size
2112
starexec-result
MAYBE
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o 2ndsneg : [o * o] --> o 2ndspos : [o * o] --> o cons : [o * o] --> o from : [o] --> o negrecip : [o] --> o pi : [o] --> o plus : [o * o] --> o posrecip : [o] --> o rcons : [o * o] --> o rnil : [] --> o s : [o] --> o square : [o] --> o times : [o * o] --> o from(X) => cons(X, from(s(X))) 2ndspos(0, X) => rnil 2ndspos(s(X), cons(Y, cons(Z, U))) => rcons(posrecip(Z), 2ndsneg(X, U)) 2ndsneg(0, X) => rnil 2ndsneg(s(X), cons(Y, cons(Z, U))) => rcons(negrecip(Z), 2ndspos(X, U)) pi(X) => 2ndspos(X, from(0)) plus(0, X) => X plus(s(X), Y) => s(plus(X, Y)) times(0, X) => 0 times(s(X), Y) => plus(Y, times(X, Y)) square(X) => times(X, X) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> nd 2ndsneg : [nd * ac] --> bc 2ndspos : [nd * ac] --> bc cons : [nd * ac] --> ac from : [nd] --> ac negrecip : [nd] --> pb pi : [nd] --> bc plus : [nd * nd] --> nd posrecip : [nd] --> pb rcons : [pb * bc] --> bc rnil : [] --> bc s : [nd] --> nd square : [nd] --> nd times : [nd * nd] --> nd +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995.
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