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TRS Stand 20472 pair #381710925
details
property
value
status
complete
benchmark
#3.55.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0921928882599 seconds
cpu usage
0.093234441
max memory
4861952.0
stage attributes
key
value
output-size
24549
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 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)) 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 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) quicksort(nil) -> nil quot(0,s(y)) -> 0 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(add(n,x),y) -> add(n,app(x,y)) app(nil,y) -> y 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)) 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 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) quicksort(nil) -> nil quot(0,s(y)) -> 0 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) -> 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) 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) MINUS(s(x),s(y)) -> MINUS(x,y) QUICKSORT(add(n,x)) -> APP(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) QUICKSORT(add(n,x)) -> HIGH(n,x) QUICKSORT(add(n,x)) -> LOW(n,x) QUICKSORT(add(n,x)) -> QUICKSORT(high(n,x)) QUICKSORT(add(n,x)) -> QUICKSORT(low(n,x)) QUOT(s(x),s(y)) -> MINUS(x,y) QUOT(s(x),s(y)) -> QUOT(minus(x,y),s(y)) -> Rules: app(add(n,x),y) -> add(n,app(x,y)) app(nil,y) -> y 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)) 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 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) quicksort(nil) -> nil quot(0,s(y)) -> 0
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