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TRS Stand 20472 pair #381711900
details
property
value
status
complete
benchmark
#4.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.183668851852 seconds
cpu usage
0.185674728
max memory
7299072.0
stage attributes
key
value
output-size
25216
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 l l' s s' t t' x x' y z) (RULES and(false,y) -> false and(true,y) -> y eq(apply(t,s),apply(t',s')) -> and(eq(t,t'),eq(s,s')) eq(apply(t,s),lambda(x,t)) -> false eq(apply(t,s),var(l)) -> false eq(cons(t,l),cons(t',l')) -> and(eq(t,t'),eq(l,l')) eq(cons(t,l),nil) -> false eq(lambda(x,t),apply(t,s)) -> false eq(lambda(x,t),lambda(x',t')) -> and(eq(x,x'),eq(t,t')) eq(lambda(x,t),var(l)) -> false eq(nil,cons(t,l)) -> false eq(nil,nil) -> true eq(var(l),apply(t,s)) -> false eq(var(l),lambda(x,t)) -> false eq(var(l),var(l')) -> eq(l,l') if(false,var(k),var(l')) -> var(l') if(true,var(k),var(l')) -> var(k) ren(var(l),var(k),var(l')) -> if(eq(l,l'),var(k),var(l')) ren(x,y,apply(t,s)) -> apply(ren(x,y,t),ren(x,y,s)) ren(x,y,lambda(z,t)) -> lambda(var(cons(x,cons(y,cons(lambda(z,t),nil)))),ren(x,y,ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil)))),t))) ) Problem 1: Innermost Equivalent Processor: -> Rules: and(false,y) -> false and(true,y) -> y eq(apply(t,s),apply(t',s')) -> and(eq(t,t'),eq(s,s')) eq(apply(t,s),lambda(x,t)) -> false eq(apply(t,s),var(l)) -> false eq(cons(t,l),cons(t',l')) -> and(eq(t,t'),eq(l,l')) eq(cons(t,l),nil) -> false eq(lambda(x,t),apply(t,s)) -> false eq(lambda(x,t),lambda(x',t')) -> and(eq(x,x'),eq(t,t')) eq(lambda(x,t),var(l)) -> false eq(nil,cons(t,l)) -> false eq(nil,nil) -> true eq(var(l),apply(t,s)) -> false eq(var(l),lambda(x,t)) -> false eq(var(l),var(l')) -> eq(l,l') if(false,var(k),var(l')) -> var(l') if(true,var(k),var(l')) -> var(k) ren(var(l),var(k),var(l')) -> if(eq(l,l'),var(k),var(l')) ren(x,y,apply(t,s)) -> apply(ren(x,y,t),ren(x,y,s)) ren(x,y,lambda(z,t)) -> lambda(var(cons(x,cons(y,cons(lambda(z,t),nil)))),ren(x,y,ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil)))),t))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EQ(apply(t,s),apply(t',s')) -> AND(eq(t,t'),eq(s,s')) EQ(apply(t,s),apply(t',s')) -> EQ(s,s') EQ(apply(t,s),apply(t',s')) -> EQ(t,t') EQ(cons(t,l),cons(t',l')) -> AND(eq(t,t'),eq(l,l')) EQ(cons(t,l),cons(t',l')) -> EQ(l,l') EQ(cons(t,l),cons(t',l')) -> EQ(t,t') EQ(lambda(x,t),lambda(x',t')) -> AND(eq(x,x'),eq(t,t')) EQ(lambda(x,t),lambda(x',t')) -> EQ(t,t') EQ(lambda(x,t),lambda(x',t')) -> EQ(x,x') EQ(var(l),var(l')) -> EQ(l,l') REN(var(l),var(k),var(l')) -> EQ(l,l') REN(var(l),var(k),var(l')) -> IF(eq(l,l'),var(k),var(l')) REN(x,y,apply(t,s)) -> REN(x,y,s) REN(x,y,apply(t,s)) -> REN(x,y,t) REN(x,y,lambda(z,t)) -> REN(x,y,ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil)))),t)) REN(x,y,lambda(z,t)) -> REN(z,var(cons(x,cons(y,cons(lambda(z,t),nil)))),t) -> Rules: and(false,y) -> false and(true,y) -> y eq(apply(t,s),apply(t',s')) -> and(eq(t,t'),eq(s,s')) eq(apply(t,s),lambda(x,t)) -> false eq(apply(t,s),var(l)) -> false eq(cons(t,l),cons(t',l')) -> and(eq(t,t'),eq(l,l')) eq(cons(t,l),nil) -> false eq(lambda(x,t),apply(t,s)) -> false eq(lambda(x,t),lambda(x',t')) -> and(eq(x,x'),eq(t,t')) eq(lambda(x,t),var(l)) -> false eq(nil,cons(t,l)) -> false eq(nil,nil) -> true eq(var(l),apply(t,s)) -> false eq(var(l),lambda(x,t)) -> false eq(var(l),var(l')) -> eq(l,l') if(false,var(k),var(l')) -> var(l') if(true,var(k),var(l')) -> var(k) ren(var(l),var(k),var(l')) -> if(eq(l,l'),var(k),var(l'))
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