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TRS Stand 20472 pair #381714387
details
property
value
status
complete
benchmark
MYNAT_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.63387513161 seconds
cpu usage
1.625113442
max memory
4.6362624E7
stage attributes
key
value
output-size
46029
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o * o] --> o U12 : [o * o] --> o U13 : [o] --> o U21 : [o * o] --> o U22 : [o] --> o U31 : [o * o * o] --> o U32 : [o * o] --> o U33 : [o] --> o U41 : [o * o] --> o U51 : [o * o * o] --> o U61 : [o] --> o U71 : [o * o * o] --> o activate : [o] --> o and : [o * o] --> o isNat : [o] --> o isNatKind : [o] --> o n!6220!62200 : [] --> o n!6220!6220and : [o * o] --> o n!6220!6220isNatKind : [o] --> o n!6220!6220plus : [o * o] --> o n!6220!6220s : [o] --> o n!6220!6220x : [o * o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o x : [o * o] --> o U11(tt, X, Y) => U12(isNat(activate(X)), activate(Y)) U12(tt, X) => U13(isNat(activate(X))) U13(tt) => tt U21(tt, X) => U22(isNat(activate(X))) U22(tt) => tt U31(tt, X, Y) => U32(isNat(activate(X)), activate(Y)) U32(tt, X) => U33(isNat(activate(X))) U33(tt) => tt U41(tt, X) => activate(X) U51(tt, X, Y) => s(plus(activate(Y), activate(X))) U61(tt) => 0 U71(tt, X, Y) => plus(x(activate(Y), activate(X)), activate(Y)) and(tt, X) => activate(X) isNat(n!6220!62200) => tt isNat(n!6220!6220plus(X, Y)) => U11(and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))), activate(X), activate(Y)) isNat(n!6220!6220s(X)) => U21(isNatKind(activate(X)), activate(X)) isNat(n!6220!6220x(X, Y)) => U31(and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))), activate(X), activate(Y)) isNatKind(n!6220!62200) => tt isNatKind(n!6220!6220plus(X, Y)) => and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))) isNatKind(n!6220!6220s(X)) => isNatKind(activate(X)) isNatKind(n!6220!6220x(X, Y)) => and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))) plus(X, 0) => U41(and(isNat(X), n!6220!6220isNatKind(X)), X) plus(X, s(Y)) => U51(and(and(isNat(Y), n!6220!6220isNatKind(Y)), n!6220!6220and(isNat(X), n!6220!6220isNatKind(X))), Y, X) x(X, 0) => U61(and(isNat(X), n!6220!6220isNatKind(X))) x(X, s(Y)) => U71(and(and(isNat(Y), n!6220!6220isNatKind(Y)), n!6220!6220and(isNat(X), n!6220!6220isNatKind(X))), Y, X) 0 => n!6220!62200 plus(X, Y) => n!6220!6220plus(X, Y) isNatKind(X) => n!6220!6220isNatKind(X) s(X) => n!6220!6220s(X) x(X, Y) => n!6220!6220x(X, Y) and(X, Y) => n!6220!6220and(X, Y) activate(n!6220!62200) => 0 activate(n!6220!6220plus(X, Y)) => plus(X, Y) activate(n!6220!6220isNatKind(X)) => isNatKind(X) activate(n!6220!6220s(X)) => s(X) activate(n!6220!6220x(X, Y)) => x(X, Y) activate(n!6220!6220and(X, Y)) => and(X, Y) activate(X) => X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): U11(tt, X, Y) >? U12(isNat(activate(X)), activate(Y)) U12(tt, X) >? U13(isNat(activate(X))) U13(tt) >? tt U21(tt, X) >? U22(isNat(activate(X))) U22(tt) >? tt U31(tt, X, Y) >? U32(isNat(activate(X)), activate(Y)) U32(tt, X) >? U33(isNat(activate(X))) U33(tt) >? tt U41(tt, X) >? activate(X) U51(tt, X, Y) >? s(plus(activate(Y), activate(X))) U61(tt) >? 0 U71(tt, X, Y) >? plus(x(activate(Y), activate(X)), activate(Y)) and(tt, X) >? activate(X) isNat(n!6220!62200) >? tt isNat(n!6220!6220plus(X, Y)) >? U11(and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))), activate(X), activate(Y)) isNat(n!6220!6220s(X)) >? U21(isNatKind(activate(X)), activate(X)) isNat(n!6220!6220x(X, Y)) >? U31(and(isNatKind(activate(X)), n!6220!6220isNatKind(activate(Y))), activate(X), activate(Y)) isNatKind(n!6220!62200) >? tt
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