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TRS Stand 20472 pair #381713728
details
property
value
status
complete
benchmark
sumList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.730015993118 seconds
cpu usage
0.726515065
max memory
2.7324416E7
stage attributes
key
value
output-size
2243
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 false : [] --> o head : [o] --> o if : [o * o * o * o * o * o] --> o inc : [o] --> o isEmpty : [o] --> o isZero : [o] --> o nil : [] --> o p : [o] --> o s : [o] --> o sum : [o] --> o sumList : [o * o] --> o tail : [o] --> o true : [] --> o isEmpty(cons(X, Y)) => false isEmpty(nil) => true isZero(0) => true isZero(s(X)) => false head(cons(X, Y)) => X tail(cons(X, Y)) => Y tail(nil) => nil p(s(s(X))) => s(p(s(X))) p(s(0)) => 0 p(0) => 0 inc(s(X)) => s(inc(X)) inc(0) => s(0) sumList(X, Y) => if(isEmpty(X), isZero(head(X)), Y, tail(X), cons(p(head(X)), tail(X)), inc(Y)) if(true, X, Y, Z, U, V) => Y if(false, true, X, Y, Z, U) => sumList(Y, X) if(false, false, X, Y, Z, U) => sumList(Z, U) sum(X) => sumList(X, 0) 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 : [] --> cf cons : [cf * wd] --> wd false : [] --> sd head : [wd] --> cf if : [sd * sd * cf * wd * wd * cf] --> cf inc : [cf] --> cf isEmpty : [wd] --> sd isZero : [cf] --> sd nil : [] --> wd p : [cf] --> cf s : [cf] --> cf sum : [wd] --> cf sumList : [wd * cf] --> cf tail : [wd] --> wd true : [] --> sd +++ 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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