Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381714404
details
property
value
status
complete
benchmark
thiemann06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
6.84715390205 seconds
cpu usage
6.843530922
max memory
5.2514816E7
stage attributes
key
value
output-size
2112
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 average : [o * o] --> o false : [] --> o if : [o * o * o * o * o * o] --> o if2 : [o * o * o * o * o] --> o if3 : [o * o * o * o] --> o if4 : [o * o * o] --> o le : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o p(s(X)) => X p(0) => 0 le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) average(X, Y) => if(le(X, 0), le(Y, 0), le(Y, s(0)), le(Y, s(s(0))), X, Y) if(true, X, Y, Z, U, V) => if2(X, Y, Z, U, V) if(false, X, Y, Z, U, V) => average(p(U), s(V)) if2(true, X, Y, Z, U) => 0 if2(false, X, Y, Z, U) => if3(X, Y, Z, U) if3(true, X, Y, Z) => 0 if3(false, X, Y, Z) => if4(X, Y, Z) if4(true, X, Y) => s(0) if4(false, X, Y) => average(s(X), p(p(Y))) 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 : [] --> ff average : [ff * ff] --> ff false : [] --> dc if : [dc * dc * dc * dc * ff * ff] --> ff if2 : [dc * dc * dc * ff * ff] --> ff if3 : [dc * dc * ff * ff] --> ff if4 : [dc * ff * ff] --> ff le : [ff * ff] --> dc p : [ff] --> ff s : [ff] --> ff true : [] --> dc +++ 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.
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472