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TRS Stand 20472 pair #381713258
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
n006.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0936079025269 seconds
cpu usage
0.07739116
max memory
4702208.0
stage attributes
key
value
output-size
17325
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 L M N X Y) (RULES app(cons(N,L),Y) -> cons(N,app(L,Y)) app(nil,Y) -> Y high(N,cons(M,L)) -> ifhigh(le(M,N),N,cons(M,L)) high(N,nil) -> nil ifhigh(false,N,cons(M,L)) -> cons(M,high(N,L)) ifhigh(true,N,cons(M,L)) -> high(N,L) iflow(false,N,cons(M,L)) -> low(N,L) iflow(true,N,cons(M,L)) -> cons(M,low(N,L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) low(N,cons(M,L)) -> iflow(le(M,N),N,cons(M,L)) low(N,nil) -> nil quicksort(cons(N,L)) -> app(quicksort(low(N,L)),cons(N,quicksort(high(N,L)))) quicksort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: app(cons(N,L),Y) -> cons(N,app(L,Y)) app(nil,Y) -> Y high(N,cons(M,L)) -> ifhigh(le(M,N),N,cons(M,L)) high(N,nil) -> nil ifhigh(false,N,cons(M,L)) -> cons(M,high(N,L)) ifhigh(true,N,cons(M,L)) -> high(N,L) iflow(false,N,cons(M,L)) -> low(N,L) iflow(true,N,cons(M,L)) -> cons(M,low(N,L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) low(N,cons(M,L)) -> iflow(le(M,N),N,cons(M,L)) low(N,nil) -> nil quicksort(cons(N,L)) -> app(quicksort(low(N,L)),cons(N,quicksort(high(N,L)))) 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,L),Y) -> APP(L,Y) HIGH(N,cons(M,L)) -> IFHIGH(le(M,N),N,cons(M,L)) HIGH(N,cons(M,L)) -> LE(M,N) IFHIGH(false,N,cons(M,L)) -> HIGH(N,L) IFHIGH(true,N,cons(M,L)) -> HIGH(N,L) IFLOW(false,N,cons(M,L)) -> LOW(N,L) IFLOW(true,N,cons(M,L)) -> LOW(N,L) LE(s(X),s(Y)) -> LE(X,Y) LOW(N,cons(M,L)) -> IFLOW(le(M,N),N,cons(M,L)) LOW(N,cons(M,L)) -> LE(M,N) QUICKSORT(cons(N,L)) -> APP(quicksort(low(N,L)),cons(N,quicksort(high(N,L)))) QUICKSORT(cons(N,L)) -> HIGH(N,L) QUICKSORT(cons(N,L)) -> LOW(N,L) QUICKSORT(cons(N,L)) -> QUICKSORT(high(N,L)) QUICKSORT(cons(N,L)) -> QUICKSORT(low(N,L)) -> Rules: app(cons(N,L),Y) -> cons(N,app(L,Y)) app(nil,Y) -> Y high(N,cons(M,L)) -> ifhigh(le(M,N),N,cons(M,L)) high(N,nil) -> nil ifhigh(false,N,cons(M,L)) -> cons(M,high(N,L)) ifhigh(true,N,cons(M,L)) -> high(N,L) iflow(false,N,cons(M,L)) -> low(N,L) iflow(true,N,cons(M,L)) -> cons(M,low(N,L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) low(N,cons(M,L)) -> iflow(le(M,N),N,cons(M,L)) low(N,nil) -> nil quicksort(cons(N,L)) -> app(quicksort(low(N,L)),cons(N,quicksort(high(N,L)))) quicksort(nil) -> nil Problem 1: SCC Processor: -> Pairs: APP(cons(N,L),Y) -> APP(L,Y) HIGH(N,cons(M,L)) -> IFHIGH(le(M,N),N,cons(M,L)) HIGH(N,cons(M,L)) -> LE(M,N) IFHIGH(false,N,cons(M,L)) -> HIGH(N,L) IFHIGH(true,N,cons(M,L)) -> HIGH(N,L) IFLOW(false,N,cons(M,L)) -> LOW(N,L) IFLOW(true,N,cons(M,L)) -> LOW(N,L) LE(s(X),s(Y)) -> LE(X,Y) LOW(N,cons(M,L)) -> IFLOW(le(M,N),N,cons(M,L))
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