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TRS Stand 20472 pair #381710731
details
property
value
status
complete
benchmark
minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.840799093246 seconds
cpu usage
0.779980781
max memory
3.969024E7
stage attributes
key
value
output-size
2258
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 cons : [o * o] --> o eq : [o * o] --> o false : [] --> o if1 : [o * o * o * o] --> o if2 : [o * o * o * o] --> o le : [o * o] --> o min : [o] --> o minsort : [o] --> o nil : [] --> o rm : [o * o] --> o s : [o] --> o true : [] --> o le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) eq(0, 0) => true eq(0, s(X)) => false eq(s(X), 0) => false eq(s(X), s(Y)) => eq(X, Y) minsort(nil) => nil minsort(cons(X, Y)) => cons(min(cons(X, Y)), minsort(rm(min(cons(X, Y)), cons(X, Y)))) min(nil) => 0 min(cons(X, nil)) => X min(cons(X, cons(Y, Z))) => if1(le(X, Y), X, Y, Z) if1(true, X, Y, Z) => min(cons(X, Z)) if1(false, X, Y, Z) => min(cons(Y, Z)) rm(X, nil) => nil rm(X, cons(Y, Z)) => if2(eq(X, Y), X, Y, Z) if2(true, X, Y, Z) => rm(X, Z) if2(false, X, Y, Z) => cons(Y, rm(X, Z)) 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 : [] --> oe cons : [oe * bg] --> bg eq : [oe * oe] --> df false : [] --> df if1 : [df * oe * oe * bg] --> oe if2 : [df * oe * oe * bg] --> bg le : [oe * oe] --> df min : [bg] --> oe minsort : [bg] --> bg nil : [] --> bg rm : [oe * bg] --> bg s : [oe] --> oe true : [] --> df +++ 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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