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TRS Stand 20472 pair #381710944
details
property
value
status
complete
benchmark
#4.36.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0945160388947 seconds
cpu usage
0.09397224
max memory
5308416.0
stage attributes
key
value
output-size
20278
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR k m n x) (RULES eq(0,0) -> true eq(0,s(m)) -> false eq(s(n),0) -> false eq(s(n),s(m)) -> eq(n,m) if_min(false,cons(n,cons(m,x))) -> min(cons(m,x)) if_min(true,cons(n,cons(m,x))) -> min(cons(n,x)) if_replace(false,n,m,cons(k,x)) -> cons(k,replace(n,m,x)) if_replace(true,n,m,cons(k,x)) -> cons(m,x) le(0,m) -> true le(s(n),0) -> false le(s(n),s(m)) -> le(n,m) min(cons(0,nil)) -> 0 min(cons(s(n),nil)) -> s(n) min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x))) replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x)) replace(n,m,nil) -> nil sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) sort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: eq(0,0) -> true eq(0,s(m)) -> false eq(s(n),0) -> false eq(s(n),s(m)) -> eq(n,m) if_min(false,cons(n,cons(m,x))) -> min(cons(m,x)) if_min(true,cons(n,cons(m,x))) -> min(cons(n,x)) if_replace(false,n,m,cons(k,x)) -> cons(k,replace(n,m,x)) if_replace(true,n,m,cons(k,x)) -> cons(m,x) le(0,m) -> true le(s(n),0) -> false le(s(n),s(m)) -> le(n,m) min(cons(0,nil)) -> 0 min(cons(s(n),nil)) -> s(n) min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x))) replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x)) replace(n,m,nil) -> nil sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) sort(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: EQ(s(n),s(m)) -> EQ(n,m) IF_MIN(false,cons(n,cons(m,x))) -> MIN(cons(m,x)) IF_MIN(true,cons(n,cons(m,x))) -> MIN(cons(n,x)) IF_REPLACE(false,n,m,cons(k,x)) -> REPLACE(n,m,x) LE(s(n),s(m)) -> LE(n,m) MIN(cons(n,cons(m,x))) -> IF_MIN(le(n,m),cons(n,cons(m,x))) MIN(cons(n,cons(m,x))) -> LE(n,m) REPLACE(n,m,cons(k,x)) -> EQ(n,k) REPLACE(n,m,cons(k,x)) -> IF_REPLACE(eq(n,k),n,m,cons(k,x)) SORT(cons(n,x)) -> MIN(cons(n,x)) SORT(cons(n,x)) -> REPLACE(min(cons(n,x)),n,x) SORT(cons(n,x)) -> SORT(replace(min(cons(n,x)),n,x)) -> Rules: eq(0,0) -> true eq(0,s(m)) -> false eq(s(n),0) -> false eq(s(n),s(m)) -> eq(n,m) if_min(false,cons(n,cons(m,x))) -> min(cons(m,x)) if_min(true,cons(n,cons(m,x))) -> min(cons(n,x)) if_replace(false,n,m,cons(k,x)) -> cons(k,replace(n,m,x)) if_replace(true,n,m,cons(k,x)) -> cons(m,x) le(0,m) -> true le(s(n),0) -> false le(s(n),s(m)) -> le(n,m) min(cons(0,nil)) -> 0 min(cons(s(n),nil)) -> s(n) min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x))) replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x)) replace(n,m,nil) -> nil sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) sort(nil) -> nil Problem 1: SCC Processor: -> Pairs: EQ(s(n),s(m)) -> EQ(n,m) IF_MIN(false,cons(n,cons(m,x))) -> MIN(cons(m,x)) IF_MIN(true,cons(n,cons(m,x))) -> MIN(cons(n,x))
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