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TRS Stand 20472 pair #381714126
details
property
value
status
complete
benchmark
thiemann16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.93635392189 seconds
cpu usage
0.932928097
max memory
4.2995712E7
stage attributes
key
value
output-size
2125
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 check : [o] --> o even : [] --> o half : [o] --> o if : [o * o * o * o * o] --> o odd : [] --> o p : [o] --> o plus : [o * o] --> o s : [o] --> o times : [o * o] --> o timesIter : [o * o * o] --> o zero : [] --> o check(0) => zero check(s(0)) => odd check(s(s(0))) => even check(s(s(s(X)))) => check(s(X)) half(0) => 0 half(s(0)) => 0 half(s(s(X))) => s(half(X)) plus(0, X) => X plus(s(X), Y) => s(plus(X, Y)) times(X, Y) => timesIter(X, Y, 0) timesIter(X, Y, Z) => if(check(X), X, Y, Z, plus(Z, Y)) p(s(X)) => X p(0) => 0 if(zero, X, Y, Z, U) => Z if(odd, X, Y, Z, U) => timesIter(p(X), Y, U) if(even, X, Y, Z, U) => plus(timesIter(half(X), Y, half(Z)), timesIter(half(X), Y, half(s(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 : [] --> bf check : [bf] --> uc even : [] --> uc half : [bf] --> bf if : [uc * bf * bf * bf * bf] --> bf odd : [] --> uc p : [bf] --> bf plus : [bf * bf] --> bf s : [bf] --> bf times : [bf * bf] --> bf timesIter : [bf * bf * bf] --> bf zero : [] --> uc +++ 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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