details

property	value
status	complete
benchmark	quicksort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.854824066162 seconds
cpu usage	0.756891141
max memory	1.325056E7

stage attributes

key	value
output-size	27182
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 m:S n:S x:S y:S) (RULES app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S head(add(n:S,x:S)) -> n:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) if_qs(ffalse,x:S,n:S,y:S) -> app(quicksort(x:S),add(n:S,quicksort(y:S))) if_qs(ttrue,x:S,n:S,y:S) -> nil isempty(add(n:S,x:S)) -> ffalse isempty(nil) -> ttrue le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) low(n:S,add(m:S,x:S)) -> if_low(le(m:S,n:S),n:S,add(m:S,x:S)) low(n:S,nil) -> nil quicksort(x:S) -> if_qs(isempty(x:S),low(head(x:S),tail(x:S)),head(x:S),high(head(x:S),tail(x:S))) tail(add(n:S,x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S head(add(n:S,x:S)) -> n:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) if_qs(ffalse,x:S,n:S,y:S) -> app(quicksort(x:S),add(n:S,quicksort(y:S))) if_qs(ttrue,x:S,n:S,y:S) -> nil isempty(add(n:S,x:S)) -> ffalse isempty(nil) -> ttrue le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) low(n:S,add(m:S,x:S)) -> if_low(le(m:S,n:S),n:S,add(m:S,x:S)) low(n:S,nil) -> nil quicksort(x:S) -> if_qs(isempty(x:S),low(head(x:S),tail(x:S)),head(x:S),high(head(x:S),tail(x:S))) tail(add(n:S,x:S)) -> x:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(add(n:S,x:S),y:S) -> APP(x:S,y:S) HIGH(n:S,add(m:S,x:S)) -> IF_HIGH(le(m:S,n:S),n:S,add(m:S,x:S)) HIGH(n:S,add(m:S,x:S)) -> LE(m:S,n:S) IF_HIGH(ffalse,n:S,add(m:S,x:S)) -> HIGH(n:S,x:S) IF_HIGH(ttrue,n:S,add(m:S,x:S)) -> HIGH(n:S,x:S) IF_LOW(ffalse,n:S,add(m:S,x:S)) -> LOW(n:S,x:S) IF_LOW(ttrue,n:S,add(m:S,x:S)) -> LOW(n:S,x:S) IF_QS(ffalse,x:S,n:S,y:S) -> APP(quicksort(x:S),add(n:S,quicksort(y:S))) IF_QS(ffalse,x:S,n:S,y:S) -> QUICKSORT(x:S) IF_QS(ffalse,x:S,n:S,y:S) -> QUICKSORT(y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOW(n:S,add(m:S,x:S)) -> IF_LOW(le(m:S,n:S),n:S,add(m:S,x:S)) LOW(n:S,add(m:S,x:S)) -> LE(m:S,n:S) QUICKSORT(x:S) -> HEAD(x:S) QUICKSORT(x:S) -> HIGH(head(x:S),tail(x:S)) QUICKSORT(x:S) -> IF_QS(isempty(x:S),low(head(x:S),tail(x:S)),head(x:S),high(head(x:S),tail(x:S))) QUICKSORT(x:S) -> ISEMPTY(x:S) QUICKSORT(x:S) -> LOW(head(x:S),tail(x:S)) QUICKSORT(x:S) -> TAIL(x:S) -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S head(add(n:S,x:S)) -> n:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) if_qs(ffalse,x:S,n:S,y:S) -> app(quicksort(x:S),add(n:S,quicksort(y:S))) if_qs(ttrue,x:S,n:S,y:S) -> nil isempty(add(n:S,x:S)) -> ffalse isempty(nil) -> ttrue le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse popout

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actions

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