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TRS Stand 20472 pair #381714484
details
property
value
status
complete
benchmark
otto13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.18327307701 seconds
cpu usage
1.171470155
max memory
3.47136E7
stage attributes
key
value
output-size
2028
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 double : [o] --> o false : [] --> o first : [] --> o greater : [o * o] --> o if : [o * o * o * o] --> o le : [o * o * o] --> o s : [o] --> o second : [] --> o triple : [o] --> o true : [] --> o le(0, X, Y) => greater(X, Y) le(s(X), 0, Y) => false le(s(X), s(Y), 0) => false le(s(X), s(Y), s(Z)) => le(X, Y, Z) greater(X, 0) => first greater(0, s(X)) => second greater(s(X), s(Y)) => greater(X, Y) double(0) => 0 double(s(X)) => s(s(double(X))) triple(X) => if(le(X, X, double(X)), X, 0, 0) if(false, X, Y, Z) => true if(first, X, Y, Z) => if(le(s(X), Y, s(Z)), s(X), Y, s(Z)) if(second, X, Y, Z) => if(le(s(X), s(Y), Z), s(X), s(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 : [] --> pe double : [pe] --> pe false : [] --> le first : [] --> le greater : [pe * pe] --> le if : [le * pe * pe * pe] --> re le : [pe * pe * pe] --> le s : [pe] --> pe second : [] --> le triple : [pe] --> re true : [] --> re +++ 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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