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TRS Stand 20472 pair #381710226
details
property
value
status
complete
benchmark
parting03_minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.570044994354 seconds
cpu usage
0.566800966
max memory
2.9966336E7
stage attributes
key
value
output-size
2210
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 del : [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] --> o minsort : [o] --> o nil : [] --> 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) if1(true, X, Y, Z) => min(X, Z) if1(false, X, Y, Z) => min(Y, Z) if2(true, X, Y, Z) => Z if2(false, X, Y, Z) => cons(Y, del(X, Z)) minsort(nil) => nil minsort(cons(X, Y)) => cons(min(X, Y), minsort(del(min(X, Y), cons(X, Y)))) min(X, nil) => X min(X, cons(Y, Z)) => if1(le(X, Y), X, Y, Z) del(X, nil) => nil del(X, cons(Y, Z)) => if2(eq(X, Y), X, Y, 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 : [] --> pf cons : [pf * pf] --> pf del : [pf * pf] --> pf eq : [pf * pf] --> lf false : [] --> lf if1 : [lf * pf * pf * pf] --> pf if2 : [lf * pf * pf * pf] --> pf le : [pf * pf] --> lf min : [pf * pf] --> pf minsort : [pf] --> pf nil : [] --> pf s : [pf] --> pf true : [] --> lf +++ 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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