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TRS Standard pair #516960896
details
property
value
status
complete
benchmark
thiemann08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.143095016479 seconds
cpu usage
0.10464247
max memory
3964928.0
stage attributes
key
value
output-size
9076
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S l:S x:S y:S) (RULES empty(cons(x:S,l:S)) -> ffalse empty(nil) -> ttrue head(cons(x:S,l:S)) -> x:S if(ffalse,x:S,l:S) -> last(head(l:S),tail(l:S)) if(ttrue,x:S,l:S) -> x:S last(x:S,l:S) -> if(empty(l:S),x:S,l:S) rev(cons(x:S,l:S)) -> cons(rev1(x:S,l:S),rev2(x:S,l:S)) rev(nil) -> nil rev2(x:S,cons(y:S,l:S)) -> rev(cons(x:S,rev2(y:S,l:S))) rev2(x:S,nil) -> nil tail(cons(x:S,l:S)) -> l:S tail(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: empty(cons(x:S,l:S)) -> ffalse empty(nil) -> ttrue head(cons(x:S,l:S)) -> x:S if(ffalse,x:S,l:S) -> last(head(l:S),tail(l:S)) if(ttrue,x:S,l:S) -> x:S last(x:S,l:S) -> if(empty(l:S),x:S,l:S) rev(cons(x:S,l:S)) -> cons(rev1(x:S,l:S),rev2(x:S,l:S)) rev(nil) -> nil rev2(x:S,cons(y:S,l:S)) -> rev(cons(x:S,rev2(y:S,l:S))) rev2(x:S,nil) -> nil tail(cons(x:S,l:S)) -> l:S tail(nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: IF(ffalse,x:S,l:S) -> HEAD(l:S) IF(ffalse,x:S,l:S) -> LAST(head(l:S),tail(l:S)) IF(ffalse,x:S,l:S) -> TAIL(l:S) LAST(x:S,l:S) -> EMPTY(l:S) LAST(x:S,l:S) -> IF(empty(l:S),x:S,l:S) REV(cons(x:S,l:S)) -> REV2(x:S,l:S) REV2(x:S,cons(y:S,l:S)) -> REV(cons(x:S,rev2(y:S,l:S))) REV2(x:S,cons(y:S,l:S)) -> REV2(y:S,l:S) -> Rules: empty(cons(x:S,l:S)) -> ffalse empty(nil) -> ttrue head(cons(x:S,l:S)) -> x:S if(ffalse,x:S,l:S) -> last(head(l:S),tail(l:S)) if(ttrue,x:S,l:S) -> x:S last(x:S,l:S) -> if(empty(l:S),x:S,l:S) rev(cons(x:S,l:S)) -> cons(rev1(x:S,l:S),rev2(x:S,l:S)) rev(nil) -> nil rev2(x:S,cons(y:S,l:S)) -> rev(cons(x:S,rev2(y:S,l:S))) rev2(x:S,nil) -> nil tail(cons(x:S,l:S)) -> l:S tail(nil) -> nil Problem 1: SCC Processor: -> Pairs: IF(ffalse,x:S,l:S) -> HEAD(l:S) IF(ffalse,x:S,l:S) -> LAST(head(l:S),tail(l:S)) IF(ffalse,x:S,l:S) -> TAIL(l:S) LAST(x:S,l:S) -> EMPTY(l:S) LAST(x:S,l:S) -> IF(empty(l:S),x:S,l:S) REV(cons(x:S,l:S)) -> REV2(x:S,l:S) REV2(x:S,cons(y:S,l:S)) -> REV(cons(x:S,rev2(y:S,l:S))) REV2(x:S,cons(y:S,l:S)) -> REV2(y:S,l:S) -> Rules: empty(cons(x:S,l:S)) -> ffalse empty(nil) -> ttrue head(cons(x:S,l:S)) -> x:S if(ffalse,x:S,l:S) -> last(head(l:S),tail(l:S)) if(ttrue,x:S,l:S) -> x:S last(x:S,l:S) -> if(empty(l:S),x:S,l:S) rev(cons(x:S,l:S)) -> cons(rev1(x:S,l:S),rev2(x:S,l:S)) rev(nil) -> nil rev2(x:S,cons(y:S,l:S)) -> rev(cons(x:S,rev2(y:S,l:S))) rev2(x:S,nil) -> nil tail(cons(x:S,l:S)) -> l:S tail(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: REV(cons(x:S,l:S)) -> REV2(x:S,l:S)
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