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	n187.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.104663 seconds
cpu usage	0.107153
user time	0.061314
system time	0.045839
max virtual memory	113188.0
max residence set size	5880.0

stage attributes

key	value
starexec-result	YES

output

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) 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 popout

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