details

property	value
status	complete
benchmark	quick.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.094771 seconds
cpu usage	0.093281
user time	0.059527
system time	0.033754
max virtual memory	113188.0
max residence set size	9180.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S L:S M:S N:S X:S Y:S) (RULES app(cons(N:S,L:S),Y:S) -> cons(N:S,app(L:S,Y:S)) app(nil,Y:S) -> Y:S high(N:S,cons(M:S,L:S)) -> ifhigh(le(M:S,N:S),N:S,cons(M:S,L:S)) high(N:S,nil) -> nil ifhigh(ffalse,N:S,cons(M:S,L:S)) -> cons(M:S,high(N:S,L:S)) ifhigh(ttrue,N:S,cons(M:S,L:S)) -> high(N:S,L:S) iflow(ffalse,N:S,cons(M:S,L:S)) -> low(N:S,L:S) iflow(ttrue,N:S,cons(M:S,L:S)) -> cons(M:S,low(N:S,L:S)) 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,cons(M:S,L:S)) -> iflow(le(M:S,N:S),N:S,cons(M:S,L:S)) low(N:S,nil) -> nil quicksort(cons(N:S,L:S)) -> app(quicksort(low(N:S,L:S)),cons(N:S,quicksort(high(N:S,L:S)))) quicksort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: app(cons(N:S,L:S),Y:S) -> cons(N:S,app(L:S,Y:S)) app(nil,Y:S) -> Y:S high(N:S,cons(M:S,L:S)) -> ifhigh(le(M:S,N:S),N:S,cons(M:S,L:S)) high(N:S,nil) -> nil ifhigh(ffalse,N:S,cons(M:S,L:S)) -> cons(M:S,high(N:S,L:S)) ifhigh(ttrue,N:S,cons(M:S,L:S)) -> high(N:S,L:S) iflow(ffalse,N:S,cons(M:S,L:S)) -> low(N:S,L:S) iflow(ttrue,N:S,cons(M:S,L:S)) -> cons(M:S,low(N:S,L:S)) 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,cons(M:S,L:S)) -> iflow(le(M:S,N:S),N:S,cons(M:S,L:S)) low(N:S,nil) -> nil quicksort(cons(N:S,L:S)) -> app(quicksort(low(N:S,L:S)),cons(N:S,quicksort(high(N:S,L:S)))) quicksort(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: APP(cons(N:S,L:S),Y:S) -> APP(L:S,Y:S) HIGH(N:S,cons(M:S,L:S)) -> IFHIGH(le(M:S,N:S),N:S,cons(M:S,L:S)) HIGH(N:S,cons(M:S,L:S)) -> LE(M:S,N:S) IFHIGH(ffalse,N:S,cons(M:S,L:S)) -> HIGH(N:S,L:S) IFHIGH(ttrue,N:S,cons(M:S,L:S)) -> HIGH(N:S,L:S) IFLOW(ffalse,N:S,cons(M:S,L:S)) -> LOW(N:S,L:S) IFLOW(ttrue,N:S,cons(M:S,L:S)) -> LOW(N:S,L:S) LE(s(X:S),s(Y:S)) -> LE(X:S,Y:S) LOW(N:S,cons(M:S,L:S)) -> IFLOW(le(M:S,N:S),N:S,cons(M:S,L:S)) LOW(N:S,cons(M:S,L:S)) -> LE(M:S,N:S) QUICKSORT(cons(N:S,L:S)) -> APP(quicksort(low(N:S,L:S)),cons(N:S,quicksort(high(N:S,L:S)))) QUICKSORT(cons(N:S,L:S)) -> HIGH(N:S,L:S) QUICKSORT(cons(N:S,L:S)) -> LOW(N:S,L:S) QUICKSORT(cons(N:S,L:S)) -> QUICKSORT(high(N:S,L:S)) QUICKSORT(cons(N:S,L:S)) -> QUICKSORT(low(N:S,L:S)) -> Rules: app(cons(N:S,L:S),Y:S) -> cons(N:S,app(L:S,Y:S)) app(nil,Y:S) -> Y:S high(N:S,cons(M:S,L:S)) -> ifhigh(le(M:S,N:S),N:S,cons(M:S,L:S)) high(N:S,nil) -> nil ifhigh(ffalse,N:S,cons(M:S,L:S)) -> cons(M:S,high(N:S,L:S)) ifhigh(ttrue,N:S,cons(M:S,L:S)) -> high(N:S,L:S) iflow(ffalse,N:S,cons(M:S,L:S)) -> low(N:S,L:S) iflow(ttrue,N:S,cons(M:S,L:S)) -> cons(M:S,low(N:S,L:S)) 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,cons(M:S,L:S)) -> iflow(le(M:S,N:S),N:S,cons(M:S,L:S)) low(N:S,nil) -> nil quicksort(cons(N:S,L:S)) -> app(quicksort(low(N:S,L:S)),cons(N:S,quicksort(high(N:S,L:S)))) quicksort(nil) -> nil Problem 1: SCC Processor: -> Pairs: APP(cons(N:S,L:S),Y:S) -> APP(L:S,Y:S) HIGH(N:S,cons(M:S,L:S)) -> IFHIGH(le(M:S,N:S),N:S,cons(M:S,L:S)) HIGH(N:S,cons(M:S,L:S)) -> LE(M:S,N:S) IFHIGH(ffalse,N:S,cons(M:S,L:S)) -> HIGH(N:S,L:S) IFHIGH(ttrue,N:S,cons(M:S,L:S)) -> HIGH(N:S,L:S) IFLOW(ffalse,N:S,cons(M:S,L:S)) -> LOW(N:S,L:S) IFLOW(ttrue,N:S,cons(M:S,L:S)) -> LOW(N:S,L:S) LE(s(X:S),s(Y:S)) -> LE(X:S,Y:S) LOW(N:S,cons(M:S,L:S)) -> IFLOW(le(M:S,N:S),N:S,cons(M:S,L:S)) LOW(N:S,cons(M:S,L:S)) -> LE(M:S,N:S) QUICKSORT(cons(N:S,L:S)) -> APP(quicksort(low(N:S,L:S)),cons(N:S,quicksort(high(N:S,L:S)))) QUICKSORT(cons(N:S,L:S)) -> HIGH(N:S,L:S) QUICKSORT(cons(N:S,L:S)) -> LOW(N:S,L:S) QUICKSORT(cons(N:S,L:S)) -> QUICKSORT(high(N:S,L:S)) QUICKSORT(cons(N:S,L:S)) -> QUICKSORT(low(N:S,L:S)) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard