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TRS Stand 20472 pair #381711738
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
n041.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.666436910629 seconds
cpu usage
0.561893359
max memory
1.2230656E7
stage attributes
key
value
output-size
22090
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 m n x y) (RULES app(add(n,x),y) -> add(n,app(x,y)) app(nil,y) -> y head(add(n,x)) -> n high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) high(n,nil) -> nil if_high(false,n,add(m,x)) -> add(m,high(n,x)) if_high(true,n,add(m,x)) -> high(n,x) if_low(false,n,add(m,x)) -> low(n,x) if_low(true,n,add(m,x)) -> add(m,low(n,x)) if_qs(false,x,n,y) -> app(quicksort(x),add(n,quicksort(y))) if_qs(true,x,n,y) -> nil isempty(add(n,x)) -> false isempty(nil) -> true le(0,y) -> true le(s(x),0) -> false le(s(x),s(y)) -> le(x,y) low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) low(n,nil) -> nil quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) tail(add(n,x)) -> x ) Problem 1: Innermost Equivalent Processor: -> Rules: app(add(n,x),y) -> add(n,app(x,y)) app(nil,y) -> y head(add(n,x)) -> n high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) high(n,nil) -> nil if_high(false,n,add(m,x)) -> add(m,high(n,x)) if_high(true,n,add(m,x)) -> high(n,x) if_low(false,n,add(m,x)) -> low(n,x) if_low(true,n,add(m,x)) -> add(m,low(n,x)) if_qs(false,x,n,y) -> app(quicksort(x),add(n,quicksort(y))) if_qs(true,x,n,y) -> nil isempty(add(n,x)) -> false isempty(nil) -> true le(0,y) -> true le(s(x),0) -> false le(s(x),s(y)) -> le(x,y) low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) low(n,nil) -> nil quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) tail(add(n,x)) -> x -> 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,x),y) -> APP(x,y) HIGH(n,add(m,x)) -> IF_HIGH(le(m,n),n,add(m,x)) HIGH(n,add(m,x)) -> LE(m,n) IF_HIGH(false,n,add(m,x)) -> HIGH(n,x) IF_HIGH(true,n,add(m,x)) -> HIGH(n,x) IF_LOW(false,n,add(m,x)) -> LOW(n,x) IF_LOW(true,n,add(m,x)) -> LOW(n,x) IF_QS(false,x,n,y) -> APP(quicksort(x),add(n,quicksort(y))) IF_QS(false,x,n,y) -> QUICKSORT(x) IF_QS(false,x,n,y) -> QUICKSORT(y) LE(s(x),s(y)) -> LE(x,y) LOW(n,add(m,x)) -> IF_LOW(le(m,n),n,add(m,x)) LOW(n,add(m,x)) -> LE(m,n) QUICKSORT(x) -> HEAD(x) QUICKSORT(x) -> HIGH(head(x),tail(x)) QUICKSORT(x) -> IF_QS(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) QUICKSORT(x) -> ISEMPTY(x) QUICKSORT(x) -> LOW(head(x),tail(x)) QUICKSORT(x) -> TAIL(x) -> Rules: app(add(n,x),y) -> add(n,app(x,y)) app(nil,y) -> y head(add(n,x)) -> n high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) high(n,nil) -> nil if_high(false,n,add(m,x)) -> add(m,high(n,x)) if_high(true,n,add(m,x)) -> high(n,x) if_low(false,n,add(m,x)) -> low(n,x) if_low(true,n,add(m,x)) -> add(m,low(n,x)) if_qs(false,x,n,y) -> app(quicksort(x),add(n,quicksort(y))) if_qs(true,x,n,y) -> nil isempty(add(n,x)) -> false isempty(nil) -> true le(0,y) -> true le(s(x),0) -> false
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