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TRS Stand 20472 pair #381710922
details
property
value
status
complete
benchmark
Ex1_GM03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.141494035721 seconds
cpu usage
0.138052734
max memory
7659520.0
stage attributes
key
value
output-size
1594
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 diff : [o * o] --> o false : [] --> o if : [o * o * o] --> o leq : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o p(0) => 0 p(s(X)) => X leq(0, X) => true leq(s(X), 0) => false leq(s(X), s(Y)) => leq(X, Y) if(true, X, Y) => X if(false, X, Y) => Y diff(X, Y) => if(leq(X, Y), 0, s(diff(p(X), 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 : [] --> tb diff : [tb * tb] --> tb false : [] --> mb if : [mb * tb * tb] --> tb leq : [tb * tb] --> mb p : [tb] --> tb s : [tb] --> tb true : [] --> mb +++ 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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